$\smallint \,\,{\rm{cose}}{{\rm{c}}^4}\,\,x\,\,dx$ is equal to

$\tan \,\,x\,\, + \,\,\frac{{{{\tan }^3}\,\,x}}{3}\,\, + \,\,c$

$ - \,\,\tan \,\,x\,\, - \,\,\frac{{{{\tan }^3}\,\,x}}{3}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

\int \,\,\mathrm{cose}{\mathrm{c}^4}\,\,x\,\,dx

is equal to

View answer and explanation

Correct option: C

- \,\,\cot \,\,x\,\, - \,\,\frac{{{{\cot }^3}\,\,x}}{3}\,\, + \,\,c

Option C (

- \,\,\cot \,x\, - \,\,\frac{{{{\cot }^3}\,x}}{3}\, + \,\,c

) is correct because it is the result of integrating

\csc^4 x

by rewriting it as

\csc^2 x (1 + \cot^2 x)

and then integrating.