$\smallint \,\,{\sin ^3}\,\,x\,\,.\,\,{\cos ^2}x\,\,dx$ is equal to

$\frac{{{{\sin }^5}\,\,x}}{5}\,\, - \,\,\frac{{{{\sin }^3}\,\,x}}{3}\,\, + \,\,c$

$\frac{{{{\sin }^5}\,\,x}}{5}\,\, + \,\,\frac{{{{\sin }^3}\,\,x}}{3}\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

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Application +4 | -1

\int \,\,{\sin ^3}\,\,x\,\,.\,\,{\cos ^2}x\,\,dx

is equal to

View answer and explanation

Correct option: C

\frac{{{{\cos }^5}\,\,x}}{5}\,\, - \,\,\frac{{{{\cos }^3}\,\,x}}{3}\,\, + \,\,c

Option C (

\frac{{{{\cos }^5}\,\,x}}{5}\,\, - \,\,\frac{{{{\cos }^3}\,\,x}}{3}\,\, + \,\,c

) is correct because it results from correctly applying u-substitution with

u = \cos x

to the given integral.