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Evaluate: inttanxsec^2xsqrt(1-tan^2x)dx...

Evaluate: `inttanxsec^2xsqrt(1-tan^2x)dx`

Text Solution

Verified by Experts

I=`inttanxsec^2xsqrt(1-tan^2x)dx`
Let `1−tan^2x=t`
=`−2tanxsec^2xdx=dt`
I=`inttanxsec^2xsqrt(1-tan^2x)dx`
I=`1/2int t^(1/2)`
=`1/2.(2/3)t^(3/2)+c`
=`1/2.(2/3)(1−tan^2x)^(3/2)+c`
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