If ${I_n} = \smallint {\tan ^n}\,\,x\,dx$ for $n \ge 2$, then ${I_n}\,\, + \,\,{I_{n - 2}}$ is equal to

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

$n\,\,{\tan ^n}\,\,x\,\, + \,\,c$

JEE MATHEMATICS MCQ: INDEFINITE INTEGRATION

1 Easy

1 of 1

Application +4 | -1

{I_n} = \int {\tan ^n}\,\,x\,dx

for

n \ge 2

, then

{I_n}\,\, + \,\,{I_{n - 2}}

is equal to

View answer and explanation

Correct option: B

\frac{{\left( {{{\tan }^{n - 1}}\,\,x} \right)}}{{n\,\, - \,\,1}}\,\, + \,\,c

Option B is correct because integrating by parts and simplifying the expression yields the given result.