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inte^(x)((1+sinx)/(1+cosx))dx=...

`inte^(x)((1+sinx)/(1+cosx))dx=`

A

`e^(x)tan(x)/(2)+C`

B

`e^(x)cot(x)/(2)+C`

C

`e^(x)sinx+C`

D

`e^(2)cosx+C`

Text Solution

Verified by Experts

The correct Answer is:
A
let `I=inte^(x)((1+sinx))/((1+cosx))dx`
`=inte^(x)[((1+2sin((x)/(2))cos((x)/(2))))/(2cos^(2)((x)/(2)))]dx`
`=inte^(x)((1)/(2)sec^(2)((x)/(2))+tan((x)/(2)))dx`
by parts
`inte^(x)(f(x)+f^(')(x))dx=e^(x)f(x)+C`
`=e^(x)tan((x)/(2))+C`
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