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inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx...

`inte^x((2tanx)/(1+tanx)+cot^2(x+pi/4))dx` is equal to (a)`e^xtan(pi/4-x)+c` (b)`e^xtan(x-pi/4)+c` (c)`e^xtan((3pi)/4-x)+c` (d) none of these

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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