If $\int \tan ^7 x d x=f(x)+\ln |\cos x|+c$, then

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

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

$f(x)=\tan ^6 x-\frac{1}{4} \tan ^4 x+\frac{1}{2} \tan ^2 x+\ln |\cos x|+c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Medium

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Application +4 | -1

\int \tan ^7 x d x=f(x)+\ln |\cos x|+c

, then

View answer and explanation

Correct option: D

f(x)

is a polynomial of degree 6 in

\tan x

Option D (

f(x)

is a polynomial of degree 6 in

\tan x

) is correct because the integral of

\tan^7 x

can be expressed as a polynomial of degree 6 in

\tan x

plus

\ln |\cos x| + c