$\smallint \,\,{\rm{cose}}{{\rm{c}}^4}\,\,x\,\,\;dx$ 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

cosec^4(x)

by rewriting it as

cosec^2(x)(1 + cot^2(x))