If $\int \tan ^7 x \mathrm{~d} x=f(x)+C$ then

$f(x)$ is a polynomial of degree 8 in $\tan x$

$f(x)$ is a polynomial of degree 5 in $\tan x$

$f(x)$ is a polynomial of degree 6 in $\tan x$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

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Application +4 | -1

\int \tan ^7 x \mathrm{~d} x=f(x)+C

then

View answer and explanation

Correct option: C

f(x)=\frac{1}{6} \tan ^6 x-\frac{1}{4} \tan ^4 x+\frac{1}{2} \tan ^2 x+\log |\cos x|+C

Option C is correct because the integral of tan⁷(x) can be found by using substitution and polynomial division.

Practice All Chapter MCQs →

\int \sin ^5 x \cos ^4 x d x=

f(x)

\int\limits_{0}^{t^2} x f(x) d x=\frac{2}{5} t^5

f\left(\frac{4}{25}\right)

\int \frac{1-7 \cos ^2 x}{\sin ^7 x \cos ^2 x} d x=\frac{f(x)}{\sin ^7 x}+C

\int {e}^{{x}^2}\left(2-\frac{1}{{x}^2}\right) {de}={e}^{{x}^2} {f}({x})+{C}

{f}\left(\frac{1}{2}\right)=2

f(1)

{C}

\int \frac{x^7}{\left(1-x^2\right)^5} d x

\int \,\frac{{a{x^3} + \,\,b{x^2} + c}}{{{x^4}}}\;\,dx