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int e^(x)((2 tanx)/(1+tanx)+cot^(2)(x+(p...

`int e^(x)((2 tanx)/(1+tanx)+cot^(2)(x+(pi)/(4)))dx` is equal to

A

`e^(x)tan((pi)/(4)-x)+c`

B

`e^(x)tan(x-(pi)/(4))+c`

C

`e^(x)tan((3pi)/(4)-x)+c`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
Putting `x^(2)=t,`
`int e^(x)((2 tanx)/(1+tanx)+tan^(2)(x-(pi)/(4)))dx`
`=int e^(x)(tan(x-(pi)/(4))+sec^(2)(x-(pi)/(4)))dx`
`=e^(x)tan(x-(pi)/(4))+C`
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