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 481-510 of 746 questions

Preparing practice and saved progress…

481 Easy
481 of 746
Application +4 | -1
∫log⁡(x+1)−log⁡xx(x+1)dx\int \frac{\log (x+1)-\log x}{x(x+1)} d x equals
View answer and explanation
Correct option: C
−12[log⁡(x+1x)]2+c-\frac{1}{2}\left[\log \left(\frac{x+1}{x}\right)\right]^2+c
Option C (−12[log⁡(x+1x)]2+c-\frac{1}{2}\left[\log \left(\frac{x+1}{x}\right)\right]^2+c) is correct because it is the result of the integration after a suitable substitution.
482 Easy
482 of 746
Application +4 | -1
∫010  ∣ x  (x−1)  (x−2)∣  dx  is   equal   to\int \nolimits_0^{10} \,\,\left| {\,x\,\,\left( {x - 1} \right)\,\,\left( {x - 2} \right)} \right|\,\,dx\,\,\mathrm{is}\,\mathrm{\;equal\;}\,\mathrm{to} is equal to
View answer and explanation
Correct option: B
1600.5
The correct answer is A (1600.5) because the integral is evaluated by splitting the integral into intervals where the function inside the absolute value is either positive or negative.
483 Easy
483 of 746
Application +4 | -1
If ∫  dx5+4  cos⁡  x=A  tan⁡−1(B  tan⁡  x/2)  +  C\int \,\,\frac{{dx}}{{5 + 4\,\,\cos \,\,x}} = A\,\,{\tan ^{ - 1}}\left( {B\,\,\tan \,\,x/2} \right)\,\, + \,\,C, then
View answer and explanation
Correct option: B
A=2/3,   B=1/3A = 2/3,\;\,B = 1/3
Option B (A=2/3,   B=1/3A = 2/3,\;\,B = 1/3) is correct because after applying trigonometric substitutions and integrating, the values of A and B match the given form.
484 Easy
484 of 746
Application +4 | -1
∫  ex(log⁡  sin⁡  x  +  cot⁡  x)  dx\int \,\,{e^x}\left( {\log \,\,\sin \,\,x\,\, + \,\,\cot \,\,x} \right)\,\,dx is equal to
View answer and explanation
Correct option: B
ex  log⁡  sin⁡  x  +  c{e^x}\,\,\log \,\,\sin \,\,x\,\, + \,\,c
Option B (ex  log⁡  sin⁡  x  +  c{e^x}\,\,\log \,\,\sin \,\,x\,\, + \,\,c) is correct because the integral matches the form ∫ex[f(x)+f′(x)]dx=exf(x)+c\int e^x [f(x) + f'(x)] dx = e^x f(x) + c, where f(x)=log⁡(sin⁡x)f(x) = \log(\sin x).
485 Easy
485 of 746
Understanding +4 | -1
∫10x9+10xlog⁡e1010x+x10dx=\int \frac{10 x^9+10^x \log _e 10}{10^x+x^{10}} d x=
View answer and explanation
Correct option: B
log⁡(10x+x10)+c\log \left(10^x+x^{10}\right)+c
Option B (log⁡(10x+x10)+c\log \left(10^x+x^{10}\right)+c) is correct because the derivative of the denominator is exactly the numerator.
486 Easy
486 of 746
Application +4 | -1
∫x9(4x2+1)6dx\int \frac{x^9}{\left(4 x^2+1\right)^6} d x is equal to
View answer and explanation
Correct option: D
110(1x2+4)−5+C\frac{1}{10}\left(\frac{1}{\mathrm{x}^2}+4\right)^{-5}+\mathrm{C}
Option D (110(1x2+4)−5+C\frac{{1}}{{10}}(\frac{{1}}{{x^2}}+4)^{-5}+C) is correct because simplifying the integral and using substitution leads to this result.
487 Easy
487 of 746
Application +4 | -1
∫dxex+e−x\int \frac{d x}{e^x+e^{-x}} equals
View answer and explanation
Correct option: C
tan⁡−1(ex)+c\tan ^{-1}\left(e^x\right)+c
Option C (tan⁡−1(ex)+c\tan^{-1}(e^x)+c) is correct because it's the result of integrating the given function after a suitable substitution.
488 Easy
488 of 746
Analyzing +4 | -1
∫  (1+x−x−1)ex+x−1  dx\int \,\,\left( {1 + x - {x^{ - 1}}} \right){e^{x + {x^{ - 1}}}}\,\,dx is equal to
View answer and explanation
Correct option: D
xex+x−1  +  cx{e^{x + {x^{ - 1}}}}\,\, + \,\,c
Option D (xex+x−1 + cx{e^{x + {x^{ - 1}}}}\, + \,c) is correct because by using integration by parts, the integral simplifies to this expression.
489 Easy
489 of 746
Application +4 | -1
If ∫dxx2(xn+1)(n−1)/n=−[f(x)]1/n+c\int \frac{d x}{x^2\left(x^n+1\right)^{(n-1) / n}}=-[f(x)]^{1 / n}+c, then f(x)f(x) is-
View answer and explanation
Correct option: B
1+x−n1+x^{-n}
Option B (1+x−n1+x^{-n}) is the correct answer because the integral evaluates to −[1+x−n]1/n+c-[1+x^{-n}]^{1/n} + c.
490 Easy
490 of 746
Application +4 | -1
∫ex−1+xe−1ex+xexdx\int {\frac{{{{\text{e}}^{x - 1}} + {x^{e - 1}}}}{{{{\text{e}}^x} + x{{\text{e}}^x}}}} {\text{dx}} is equal to
View answer and explanation
Correct option: A
1eln⁡(x2+ex)+c\frac{1}{e} \ln \left(x^2+e^x\right)+c
Option A (1eln⁡(x2+ex)+c\frac{1}{e} \ln \left(x^2+e^x\right)+c) is correct because differentiating this option yields the integrand after simplification.
491 Easy
491 of 746
Application +4 | -1
I=∫x2−1x32x4−2x2+1dxI=\int \frac{x^2-1}{x^3 \sqrt{2 x^4-2 x^2+1}} d x equal to
View answer and explanation
Correct option: D
2x4−2x2+12x2+C\frac{\sqrt{2 x^4-2 x^2+1}}{2 x^2}+C
Option D is correct because the integral can be solved by substitution after manipulating the expression.
492 Easy
492 of 746
Application +4 | -1
If ∫f(x)dx=ψ(x)\int f(x) d x=\psi(x), then ∫x5f(x3)dx\int x^5 f\left(x^3\right) d x is equal to
View answer and explanation
Correct option: C
13x3ψ(x3)−∫x2ψ(x3)dx+C\frac{1}{3} x^3 \psi\left(x^3\right)-\int x^2 \psi\left(x^3\right) d x+C
Option C (13x3ψ(x3)−∫x2ψ(x3)dx+C\frac{{1}}{{3}} x^3 \psi(x^3)-\int x^2 \psi(x^3) dx+C) is correct because it represents the result of the given integral after applying substitution and integration by parts.
493 Easy
493 of 746
Application +4 | -1
If m\mathrm{m} is an integer, then ∫0πsin⁡(2mx)sin⁡xdx\int\limits_{0}^\pi \frac{\sin (2 \mathrm{mx})}{\sin \mathrm{x}} \mathrm{dx} is equal to :
View answer and explanation
Correct option: A
0
Option A (0) is correct because the integral evaluates to zero by using the property ∫0af(x)dx=∫0af(a−x)dx\int_0^a f(x) dx = \int_0^a f(a-x) dx and showing that the integral is equal to its negative.
494 Easy
494 of 746
Application +4 | -1
∫log⁡x(1+log⁡x)2dx=\int \frac{\log x}{(1+\log x)^2} d x=
View answer and explanation
Correct option: C
x1+log⁡x+c\frac{x}{1+\log x}+c
Option C (x1+log⁡x+c\frac{{x}}{{1+\log x}}+c) is correct because the integral evaluates to this expression after substitution and simplification.
495 Easy
495 of 746
Application +4 | -1
The value of ∫3x+2(x−2)2  (x−3)  dx\int \frac{{3x + 2}}{{{{\left( {x - 2} \right)}^2}\,\,\left( {x - 3} \right)}}\;dx is
View answer and explanation
Correct option: C
11    log⁡  x−3x−2  +  8x−2+c11\,\,\;\log \,\,\frac{{x - 3}}{{x - 2}}\,\, + \,\,\frac{8}{{x - 2}} + c
Option C (11   log⁡  x−3x−2  +  8x−2+c11\,\;\log \,\,\frac{{x - 3}}{{x - 2}}\,\, + \,\,\frac{8}{{x - 2}} + c) is correct because it is the result of integrating the given rational function using partial fraction decomposition.

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
496 Easy
496 of 746
Application +4 | -1
The area bounded by the curve y=32xy=\frac{3}{2} \sqrt{x}, the line x=1{x}=1 and x{x}-axis is_____ sq. units.
View answer and explanation
Correct option: A
4
Option A (3) is correct because using the property of definite integrals, the value of the integral is 3.
497 Easy
497 of 746
Application +4 | -1
The function ff whose graph passes through (4,−20)(4,-20) and whose derivative is cos⁡(4−x)\cos (\sqrt{4-x}) is given by
View answer and explanation
Correct option: D
−(2x+12)4−xsin⁡4−x+(4−6x)cos⁡4−x-(2 x+12) \sqrt{4-x} \sin \sqrt{4-x} \\ +(4-6 x) \cos \sqrt{4-x}
Option C (−2(4−xsin⁡4−x+cos⁡4−x)−18-2(\sqrt{4-x} \sin \sqrt{4-x}+\cos \sqrt{4-x})-18) is correct because integrating the derivative and using the given point yields this function.
498 Easy
498 of 746
Application +4 | -1
The value of ∫cos⁡2xcos⁡xdx\int \frac{\cos 2 x}{\cos x} d x is equal to
View answer and explanation
Correct option: A
2sin⁡x−ℓn∣sec⁡x+tan⁡x∣+C2 \sin x-\ell n |\sec x+\tan x|+C
Option A (2sin⁡x−ℓn∣sec⁡x+tan⁡x∣+C2 \sin x-\ell n |\sec x+\tan x|+C) is correct because it follows from simplifying the integrand using trigonometric identities and then integrating.
499 Easy
499 of 746
Application +4 | -1
∫1sin⁡3x  cos⁡  xdx\int \frac{1}{{\sqrt {{{\sin }^3}x\,\,\cos \,\,x} }}dx is equal to
View answer and explanation
Correct option: A
− 2tan⁡  x+C\frac{{ - \,2}}{{\sqrt {\tan \,\,x} }} + C
Option A (− 2tan⁡  x+C\frac{{ - \,2}}{{\sqrt {\tan \,\,x} }} + C) is correct because after rewriting the integrand in terms of tan(x), a simple substitution and power rule integration yields the result.
500 Easy
500 of 746
Application +4 | -1
∫x31−x8dx=\int \frac{x^3}{\sqrt{1-x^8}} d x=
View answer and explanation
Correct option: C
14sin⁡−1(x4)+c\frac{1}{4} \sin ^{-1}\left(x^4\right)+c
Option C (14sin⁡−1(x4)+c\frac{1}{4} \sin ^{-1}\left(x^4\right)+c) is correct because it is the result of integrating the given expression using substitution.
501 Easy
501 of 746
Application +4 | -1
∫xtan⁡−1x(1+x2)3/2dx=\int \frac{x \tan ^{-1} x}{\left(1+x^2\right)^{3 / 2}} d x=
View answer and explanation
Correct option: B
x−tan⁡−1x1+x2+c\frac{x-\tan ^{-1} x}{\sqrt{1+x^2}}+c
Option C (tan⁡−1x−x1+x2+c\frac{\tan ^{-1} x-x}{\sqrt{1+x^2}}+c) is correct because substituting x=tan⁡θx = \tan \theta simplifies the integral, and integration by parts yields the correct result.
502 Easy
502 of 746
Application +4 | -1
If ∫tan⁡4x dx=Ktan⁡3x+Ltan⁡x+f(x)\int \tan ^4 x \mathrm{~d} x=K \tan ^3 x+L \tan x+f(x), then
View answer and explanation
Correct option: C
f(x)=x+Cf(x)=x+C
Option C (f(x)=x+Cf(x)=x+C) is correct because after integrating tan⁡4x\tan^4 x, the remaining term is x+Cx+C.
503 Easy
503 of 746
Analyzing +4 | -1
∫ex4(x+x3+2x5)ex2dx\int e^{x^4}\left(x+x^3+2 x^5\right) e^{x^2} d x is equal to
View answer and explanation
Correct option: D
12x2ex2ex4+C\frac{1}{2} x^2 e^{x^2} e^{x^4}+C
Option D (12x2ex2ex4+C\frac{1}{2} x^2 e^{x^2} e^{x^4}+C) is correct because by using the substitution x2=tx^2 = t and integrating by parts, the integral evaluates to 12x2ex2ex4+C\frac{1}{2} x^2 e^{x^2} e^{x^4}+C.
504 Easy
504 of 746
Understanding +4 | -1
∫xx(1+ln⁡x)dx\int x^x(1+\ln x) d x is equal to
View answer and explanation
Correct option: B
xx+cx^x+c
Option B (xx+cx^x+c) is correct because the integral of xx(1+ln⁡x)x^x(1+\ln x) is found by recognizing that it is the derivative of xxx^x.
505 Easy
505 of 746
Application +4 | -1
∫cos⁡2x(cos⁡x+sin⁡x)2dx=\int \frac{\cos 2 x}{(\cos x+\sin x)^2} d x=
View answer and explanation
Correct option: C
log⁡(cos⁡x+sin⁡x)+c\log (\cos x+\sin x)+c
Option C is correct because the integral simplifies to log⁡(cos⁡x+sin⁡x)+c\log(\cos x + \sin x) + c after using trigonometric identities and substitution.
506 Easy
506 of 746
Analyzing +4 | -1
The value of ∫ (x  +  1)2x(x2+  1) dx\int \,\frac{{{{\left( {x\,\, + \,\,1} \right)}^2}}}{{x\left( {{x^2} + \,\,1} \right)}}\,dx is equal to
View answer and explanation
Correct option: B
log⁡e  x+2  tan⁡−1  x  +  c{\log _e}\,\,x + 2\,\,{\tan ^{ - 1}}\,\,x\,\, + \,\,c
Option B (log⁡e x+2 tan⁡−1 x + c{\log _e}\,x + 2\,{\tan ^{ - 1}}\,x\, + \,c) is correct because the integrand can be split into simpler fractions, which integrate to this result.
507 Easy
507 of 746
Application +4 | -1
∫axxdx=\int \frac{a^{\sqrt{x}}}{\sqrt{x}} d x=
View answer and explanation
Correct option: B
2axlog⁡ae+c2 a^{\sqrt{x}} \log _a e+c
Option B (2axlog⁡ae+c2 a^{\sqrt{x}} \log _a e+c) is correct because it is the result of integrating the given expression using substitution and the properties of logarithms.
508 Easy
508 of 746
Application +4 | -1
The value of ∫xlog⁡x(log⁡x−1)dx\int x \log x(\log x-1) d x is equal to
View answer and explanation
Correct option: B
12(xlog⁡x−x)2+C\frac{1}{2}(x \log x-x)^2+C
Option B is correct because the integral simplifies to a form that can be directly integrated, resulting in 12(xlog⁡x−x)2+C\frac{1}{2}(x \log x-x)^2+C.
509 Easy
509 of 746
Application +4 | -1
If ∫dx(x2+1)(x2+4)=Ptan⁡−1x+Qtan⁡−1x2+c\int \frac{d x}{\left(x^2+1\right)\left(x^2+4\right)}=P \tan ^{-1} x+Q \tan ^{-1} \frac{x}{2}+c, then P+Q=P+Q=
View answer and explanation
Correct option: D
P+Q=16P+Q=\frac{1}{6}
Option D, P+Q=16P+Q=\frac{{1}}{{6}}, is correct because partial fraction decomposition and integration yield P=13P = \frac{{1}}{{3}} and Q=−16Q = -\frac{{1}}{{6}}, so their sum is 16\frac{{1}}{{6}}.
510 Easy
510 of 746
Analyzing +4 | -1
∫x2−2x4+4dx\int \frac{x^2-2}{x^4+4} d x is equal to
View answer and explanation
Correct option: C
14log⁡e(x2−2x+2x2+2x+2)+c\frac{1}{4} \log _e\left(\frac{x^2-2 x+2}{x^2+2 x+2}\right)+c
Option C is correct because the integral is solved by dividing by x2 and completing the square, leading to a logarithmic form.
Revision notes and key takeaways

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

Showing 481-510 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 →