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The integral intsqrt(cotx)e^(sqrt(sinx))...

The integral `intsqrt(cotx)e^(sqrt(sinx))sqrt(cosx)dx` equals

A

`(sqrt(tanx)e^(sqrt(sinx)))/(sqrt(cosx))+C`

B

`2e^(sqrt(sinx))+C`

C

`-(1)/(2)e^(sqrtsinx)+C`

D

`(sqrt(cotx)e^(sqrt(sinx)))/(2sqrt(cosx))+C`

Text Solution

Verified by Experts

The correct Answer is:
B
`e^(sqrt(sinx))=trArr(e^(sqrt(sinx)))/(2sqrtsinx)cosxdx=dt`
`rArr" "e^(sqrt(sinx))sqrt(cotx)sqrt(cosx)dx=2dt`
Hence `int2dt=2t+C=2e^(sqrt(sinx))+C`
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