Skip to main content
Back to INDEFINITE INTEGRATION

Your Progress

0 / 746 Answered
0
Correct
0
Incorrect
0%
Accuracy
JEE • MATHEMATICS • INDEFINITE INTEGRATION

Indefinite integration practice · Easy

Choose an answer to check it, or open “View answer” to study the explanation. Sign in to save progress to your account.

Practice format and chapter quiz

These sets use single-correct-answer MCQs. They do not cover every JEE Main or JEE Advanced question format and are not full-length mock papers.

Take a chapter quiz →
Showing 271-300 of 746 questions

Preparing practice and saved progress…

271 Easy
271 of 746
Application +4 | -1
∫sec⁡x⋅cosec⁡x2cot⁡x−sec⁡xcosec⁡xdx\int \frac{\sec x \cdot \operatorname{cosec} x}{2 \cot x-\sec x \operatorname{cosec} x} d x is equal to-
View answer and explanation
Correct option: A
12ln⁡∣sec⁡2x+tan⁡2x∣+C\frac{1}{2} \ln |\sec 2 x+\tan 2 x|+C
Option A (12ln⁡∣sec⁡2x+tan⁡2x∣+C\frac{1}{2} \ln |\sec 2 x+\tan 2 x|+C) is correct because it is the result of integrating the simplified expression.
272 Easy
272 of 746
Analyzing +4 | -1
If ∫x2+4x4+16dx=1atan⁡−1(x2−4ax)+C\int \frac{x^2+4}{x^4+16} d x=\frac{1}{a} \tan ^{-1}\left(\frac{x^2-4}{a x}\right)+C, then a=a=
View answer and explanation
Correct option: B
222 \sqrt{2}
Option B (222 \sqrt{2}) is correct because after simplifying the integral, the value of 'a' is found to be 222 \sqrt{2}.
273 Easy
273 of 746
Application +4 | -1
The value of ∫dxx+a2−x2\int \frac{d x}{x+\sqrt{a^2-x^2}}, is equal to
View answer and explanation
Correct option: A
12sin⁡−1(xa)+12log⁡∣x+a2−x2∣+C1\frac{1}{2} \sin ^{-1}\left(\frac{x}{a}\right)+\frac{1}{2} \log \left|x+\sqrt{a^2-x^2}\right|+C_1
Option A (12sin⁡−1(xa)+12log⁡∣x+a2−x2∣+C1\frac{1}{2} \sin ^{-1}(\frac{x}{a})+\frac{1}{2} \log |x+\sqrt{a^2-x^2}|+C_1) is correct because it is the result of the integral after applying the trigonometric substitution x=asin⁡θx = a \sin \theta and simplifying.
274 Easy
274 of 746
Application +4 | -1
∫1x2+4x+13dx\int \frac{1}{x^2+4 x+13} d x is equal to
View answer and explanation
Correct option: B
13tan⁡−1(x+23)\frac{1}{3} \tan ^{-1}\left(\frac{x+2}{3}\right)
Option B, 13tan⁡−1(x+23)\frac{1}{3} \tan ^{-1}\left(\frac{x+2}{3}\right), is correct because completing the square and using the arctangent integral formula leads to this result.
275 Easy
275 of 746
Analyzing +4 | -1
∫  (x3+3x2+3x+1)(x+1)5    dx\int \,\,\frac{{\left( {{x^3} + 3{x^2} + 3x + 1} \right)}}{{{{\left( {x + 1} \right)}^5}}}\,\,\;dx is equal to
View answer and explanation
Correct option: A
−  1(x+1)  +  c- \,\,\frac{1}{{\left( {x + 1} \right)}}\,\, + \,\,c
Option A ( − 1(x+1) + c\ - \,\frac{1}{{(x + 1)}}\, + \,c) is correct because the integrand simplifies to 1(x+1)2\frac{1}{{(x + 1)^2}}, and its integral is  − 1(x+1) + c\ - \,\frac{1}{{(x + 1)}}\, + \,c.
276 Easy
276 of 746
Understanding +4 | -1
If ∫dxsin⁡xcos⁡x=log⁡∣f(x)∣+C\int \frac{\mathrm{d} x}{\sin x \cos x}=\log |f(x)|+C then
View answer and explanation
Correct option: B
f(x)=tan⁡xf(x)=\tan x
Option B (f(x)=tan⁡xf(x)=\tan x) is correct because the integral evaluates to log⁡∣tan⁡x∣+C\log |\tan x| + C.
277 Easy
277 of 746
Application +4 | -1
∫sin⁡−1x(1−x2)1/2dx=\int \frac{\sin ^{-1} x}{\left(1-x^2\right)^{1 / 2}} d x=
View answer and explanation
Correct option: A
x1−x2sin⁡−1x+12log⁡(1−x2)+c\frac{x}{\sqrt{1-x^2}} \sin ^{-1} x+\frac{1}{2} \log \left(1-x^2\right)+c
Option A (x1−x2sin⁡−1x+12log⁡(1−x2)+c\frac{{x}}{{\sqrt{{1-x^2}}}} \sin^{{-1}} x + \frac{{1}}{{2}} \log (1-x^2) + c) is correct because the integral can be solved by substitution and then integration by parts.
278 Easy
278 of 746
Application +4 | -1
∫exsin⁡x(sin⁡x+2cos⁡x)dx=\int e^x \sin x(\sin x+2 \cos x) d x=
View answer and explanation
Correct option: A
exsin⁡2x+ce^x \sin ^2 x+c
Option A is correct because the integral simplifies to ∫ex(sin⁡2x+sin⁡2x)dx\int e^x(\sin^2 x + \sin 2x) dx, which directly integrates to exsin⁡2x+ce^x \sin^2 x + c.
279 Easy
279 of 746
Application +4 | -1
∫x3−3x+7x2+4dx\int \frac{x^3-3 x+7}{x^2+4} d x is equal to :
View answer and explanation
Correct option: B
x22+72tan⁡−1x2−72ln⁡(x2+4)+c\frac{x^2}{2}+\frac{7}{2} \tan ^{-1} \frac{x}{2}-\frac{7}{2} \ln \left(x^2+4\right)+c
Option B (x22+72tan⁡−1x2−72ln⁡(x2+4)+c\frac{x^2}{2}+\frac{7}{2} \tan ^{-1} \frac{x}{2}-\frac{7}{2} \ln \left(x^2+4\right)+c) is correct because after polynomial division and integrating each term, we obtain the given result.
280 Easy
280 of 746
Understanding +4 | -1
The primitive of the function f(x)=(1−1x2)ax+1x,x>0,f(x)=\left(1-\frac{1}{x^2}\right) a^{x+\frac{1}{x}}, x > 0, is
View answer and explanation
Correct option: A
ax+1xlog⁡ea\frac{a^{x+\frac{1}{x}}}{\log _e a}
Option A is correct because the primitive (indefinite integral) of the given function is found by recognizing the derivative pattern and applying the appropriate integration formula for exponential functions.
281 Easy
281 of 746
Application +4 | -1
∫  x(x2−a2)  (x2−b2)  dx\int \,\,\frac{x}{{\left( {{x^2} - {a^2}} \right)\,\,\left( {{x^2} - {b^2}} \right)}}\,\,dx is equal to
View answer and explanation
Correct option: C
12 (a2−  b2)  log⁡  ∣ x2−a2x2−b2 ∣  +  c\frac{1}{{2\,({a^2} - \,\,{b^2})}}\,\,\log \,\,\left| {\,\frac{{{x^2} - {a^2}}}{{{x^2} - {b^2}}}\,} \right|\,\, + \,\,c
Option C (12 (a2− b2)  log⁡  ∣ x2− a2x2− b2 ∣  +  c\frac{1}{{2\,({a^2} - \,{b^2})}}\,\,\log \,\,\left| {\,\frac{{{{x^2} - \,{a^2}}}}{{{{x^2} - \,{b^2}}}}}\,\right|\,\, + \,\,c) is correct because it represents the correct partial fraction decomposition and integration of the given expression.
282 Easy
282 of 746
Application +4 | -1
∫  exlog⁡a  ⋅  ex   dx\int \,\,{e^{x\log a}}\,\, \cdot \,\,{e^x}\;\,dx is equal to
View answer and explanation
Correct option: B
(ae)xlog⁡  (ae)\frac{{{{\left( {ae} \right)}^x}}}{{\log \,\,\left( {ae} \right)}}
Option B ((ae)xlog⁡  (ae)\frac{{{{\left( {ae} \right)}^x}}}{{\log \,\,\left( {ae} \right)}}) is correct because after simplifying the integrand and integrating, the result matches this option.
283 Easy
283 of 746
Application +4 | -1
If f(3x−43x+4)=x+2f\left(\frac{3 x-4}{3 x+4}\right)=x+2, then ∫f(x)dx\int f(x) d x is equal to
View answer and explanation
Correct option: B
−83log⁡e∣1−x∣+23x+C-\frac{8}{3} \log _e|1-x|+\frac{2}{3} x+C
Option B (−83log⁡e∣1−x∣+23x+C\frac{{-8}}{{3}} \log _e|1-x|+\frac{{2}}{{3}} x+C) is correct because it is the result of integrating f(x) after finding the expression for f(x).
284 Easy
284 of 746
Application +4 | -1
∫x1−x21+x2dx=\int x \sqrt{\frac{1-x^2}{1+x^2}} d x=
View answer and explanation
Correct option: A
12[sin⁡−1x2+1−x4]+c\frac{1}{2}\left[\sin ^{-1} x^2+\sqrt{1-x^4}\right]+c
Option B is correct because the integral can be solved by simplifying the expression and using a suitable substitution.
285 Easy
285 of 746
Application +4 | -1
If f(x)=1cos⁡2x1+tan⁡xf(x)=\frac{1}{\cos ^2 x \sqrt{1+\tan x}} then its antiderivative F(x)F(x) (given that F(0)=4F(0)=4 ) is
View answer and explanation
Correct option: C
2(1+tan⁡x+1)2(\sqrt{1+\tan x}+1)
Option C (2(1+tan⁡x+1)2(\sqrt{{1+\tan x}}+1)) is correct because it represents the antiderivative of the given function with the correct constant of integration.

Explore Other Chapters in MATHEMATICS

View All →
SEQUENCE OF SERIES 1764 MCQs DEFINITE INTEGRATION 1443 MCQs MATRICES 1363 MCQs PROBABILITY 1146 MCQs COMPLEX NUMBERS 980 MCQs DIFFERENTIAL EQUATIONS 977 MCQs
286 Easy
286 of 746
Application +4 | -1
∫sin⁡xsin⁡x−cos⁡xdx\int \frac{\sin x}{\sin x-\cos x} d x is equal to :
View answer and explanation
Correct option: B
x2+12log⁡(sin⁡x−cos⁡x)+c\frac{x}{2}+\frac{1}{2} \log (\sin x-\cos x)+c
Option B (x2+12log⁡(sin⁡x−cos⁡x)+c\frac{x}{2}+\frac{1}{2} \log (\sin x-\cos x)+c) is correct because it is the result of decomposing the integrand and integrating each part separately.
287 Easy
287 of 746
Application +4 | -1
∫(xx)x(2xlog⁡ex+x)dx\int\left(x^x\right)^x\left(2 x \log _e x+x\right) d x is equal to
View answer and explanation
Correct option: B
(xx)x+C\left(x^x\right)^x+C
Option B is correct because the integral simplifies to ∫d(xx2)\int d(x^{x^2}), which evaluates to (xx)x+C(x^x)^x + C.
288 Easy
288 of 746
Application +4 | -1
∫  ex(2x  −  2x2)dx\int \,\,{e^x}\left( {\frac{2}{x}\,\, - \,\,\frac{2}{{{x^2}}}} \right)dx is equal to
View answer and explanation
Correct option: C
2exx  +  c\frac{{2{e^x}}}{x}\,\, + \,\,c
Option C (2exx+c\frac{{2{e^x}}}{x} + c) is correct because the integral is of the form ∫ex[f(x)+f′(x)]dx=exf(x)+c\int e^x [f(x) + f'(x)] dx = e^x f(x) + c.
289 Easy
289 of 746
Application +4 | -1
∫sin⁡3xcos⁡2xdx=\int \sin ^3 x \cos ^2 x d x=
View answer and explanation
Correct option: A
cos⁡5x5−cos⁡3x3+c\frac{\cos ^5 x}{5}-\frac{\cos ^3 x}{3}+c
Option A is correct because the integral of sin⁡3xcos⁡2x\sin^3 x \cos^2 x can be solved by substituting t=cos⁡xt = \cos x and simplifying the resulting expression.
290 Easy
290 of 746
Application +4 | -1
If ∫4x2−4x+3dx=12log⁡e(2x−1+4x2−4x+3)+f(x)+c\int \sqrt{4 x^2-4 x+3} d x=\frac{1}{2} \log _e\left(2 x-1+\sqrt{4 x^2-4 x+3}\right)+f(x)+c and then f(x)f(x) equals
View answer and explanation
Correct option: A
2x−144x2−4x+3\frac{2 x-1}{4} \sqrt{4 x^2-4 x+3}
Option A is correct because the integral is solved by completing the square and using a standard integral formula, resulting in f(x) = (2x-1)/4 * sqrt(4x2-4x+3).
291 Easy
291 of 746
Application +4 | -1
The value of ∫sin⁡x3dx\int \sin \sqrt[3]{x} d x is
View answer and explanation
Correct option: B
3{(2−x2/3)cos⁡x1/3+2x1/3sin⁡x1/3}+C3\left\{\left(2-x^{2 / 3}\right) \cos x^{1 / 3}+2 x^{1 / 3} \sin x^{1 / 3}\right\}+C
Option D is correct because after substituting x1/3=θx^{1/3} = \theta and integrating by parts twice, we obtain the given expression.
292 Easy
292 of 746
Analyzing +4 | -1
∫{(log⁡x−1)1+(log⁡x)2}2dx\int\left\{\frac{(\log x-1)}{1+(\log x)^2}\right\}^2 d x is equal to
View answer and explanation
Correct option: B
x(log⁡x)2+1+c\frac{x}{(\log x)^2+1}+c
Option B (x(log⁡x)2+1+c\frac{x}{(\log x)^2+1}+c) is correct because it is the result of integrating the given expression using substitution and integration by parts.
293 Easy
293 of 746
Analyzing +4 | -1
If ∫cos⁡ x dxsin⁡3x(1+sin⁡6)x)2/3=f(x)(1+sin⁡6x)1/λ+c\int {\frac{{\cos \,x\,dx}}{{{{\sin }^3}x\left( {1 + {{\sin }^6}} \right)x{)^{2/3}}}} = f\left( x \right){{\left( {1 + {{\sin }^6}x} \right)}^{1/\lambda }} + c} where cc is a constant of integration, then is equal to
View answer and explanation
Correct option: C
-2
Option C (-2) is correct because by substituting t=1sin⁡6x+1=t3t = \frac{1}{{{\sin }^6}x} + 1 = {t^3} and solving the integral, we can find the value of λf(π3)\lambda f(\frac{\pi}{3}).
294 Easy
294 of 746
Application +4 | -1
∫1+cot⁡2x1+cot⁡xdx=\int \frac{1+\cot ^2 x}{1+\cot x} d x=
View answer and explanation
Correct option: A
−log⁡(1+cot⁡x)+c-\log (1+\cot x)+c
Option A (−log⁡(1+cot⁡x)+c- \log (1+\cot x)+c) is correct because the integral simplifies to this form after substitution.
295 Easy
295 of 746
Application +4 | -1
∫1+x21−x2dx=\int \frac{1+x^2}{\sqrt{1-x^2}} d x=
View answer and explanation
Correct option: A
32sin⁡−1x−12x1−x2+c\frac{3}{2} \sin ^{-1} x-\frac{1}{2} x \sqrt{1-x^2}+c
Option A is correct because the integral evaluates to 32sin⁡−1x−12x1−x2+c\frac{3}{2} \sin^{-1} x - \frac{1}{2}x \sqrt{1-x^2} + c after trigonometric substitution and simplification.
296 Easy
296 of 746
Understanding +4 | -1
If ∫dxa2−x2=sin⁡−1x3+c\int \frac{d x}{\sqrt{a^2-x^2}}=\sin ^{-1} \frac{x}{3}+c, then a=a=
View answer and explanation
Correct option: A
3
3 is the correct answer because the integral of 1/sqrt(a2 - x2) is arcsin(x/a) + c, and comparing it to the given integral, a must be 3.
297 Easy
297 of 746
Application +4 | -1
∫dx2x−x2\int {\frac{{dx}}{{\sqrt {2x - {x^2}} }}} is equal to
View answer and explanation
Correct option: C
sin⁡−1(x−1)+c{\sin ^{ - 1}}\left( {x - 1} \right) + c
Option C (sin⁡−1(x−1)+c{\sin ^{ - 1}}\left( {x - 1} \right) + c) is correct because the integral simplifies to the arcsine function after completing the square.
298 Easy
298 of 746
Application +4 | -1
∫  dxx  (log⁡   x)  (log⁡  log⁡  x)  …  (log⁡  log⁡.... x)⏟8  times\int \,\,\frac{{dx}}{{x\,\,(\log \,\,\,x)\,\,(\log \,\,\log \,\,x)\,\, \ldots \,\,\underbrace {(\log \,\,\log ....\,x)}_{8\,\,\mathrm{times}}}} is equal to
View answer and explanation
Correct option: C
(log⁡  log⁡  ....  x)⏟9  times  +  c\underbrace {(\log \,\,\log \,\,....\,\,x)}_{9\,\,\mathrm{times}}\,\, + \,\,c
Option C is correct because after repeated substitution, the integral simplifies to log(log...x) nine times + c.
299 Easy
299 of 746
Understanding +4 | -1
If ∫dx(x2+a2)2\int \frac{d x}{\left(x^2+a^2\right)^2} =1ka2{xx2+a2+1atan⁡−1xa}+C=\frac{1}{k a^2}\left\{\frac{x}{x^2+a^2}+\frac{1}{a} \tan ^{-1} \frac{x}{a}\right\}+C. Then the value of kk, is
View answer and explanation
Correct option: B
2
Option B (2) is correct because by integrating and comparing coefficients, the value of k in the given integral is found to be 2.
300 Easy
300 of 746
Application +4 | -1
∫cos⁡{2tan⁡−11−x1+x}dx\int \cos \left\{2 \tan ^{-1} \sqrt{\frac{1-x}{1+x}}\right\} d x is equal to
View answer and explanation
Correct option: B
12x2+k\frac{1}{2} x^2+k
Option B (12x2+k\frac{1}{2} x^2+k) is correct because it is the result of simplifying the integral after trigonometric substitution.
Revision notes and key takeaways

Review INDEFINITE INTEGRATION in your textbook or class notes, then use this set to check your understanding.

Showing 271-300 of 746 questions

Continue Your Practice

📚 More Sets in This Chapter

Try different difficulty levels to master this topic

→ ENGINEERING MATHEMATICS - INDEFINITE INTEGRATION MCQs (All) 995 MCQs → ENGINEERING MATHEMATICS - INDEFINITE INTEGRATION MCQs (Hard) 15 MCQs → ENGINEERING MATHEMATICS - INDEFINITE INTEGRATION MCQs (Medium) 411 MCQs
🎯 Next Chapters to Practice

Continue building your subject mastery

→ SEQUENCE OF SERIES 1764 MCQs → DEFINITE INTEGRATION 1443 MCQs → MATRICES 1363 MCQs → PROBABILITY 1146 MCQs

Your practice

0 / 746 answered · 746 remaining · 0% accuracy

Progress is stored on this device. Sign in to save to your account.

✓ Correct · ✗ Incorrect · ○ Unanswered

Practice settings

Type at least 2 characters or jump directly:
🩺 NEET MCQs 🔬 JEE MCQs 🎯 JEE College Predictor Study guides 📊 Dashboard
🔓

Save your learning progress

Sign in with a free account to save your practice answers and quiz results, then return to them when you revise.

Continue with Free Account →