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int(0)^(pi//2)e^(x)((1+sinx)/(1+cosx))dx...

`int_(0)^(pi//2)e^(x)((1+sinx)/(1+cosx))dx=?`

A

`0`

B

`(pi)/(4)`

C

`e^(pi//2)`

D

`(e^(pi//2)-1)`

Text Solution

AI Generated Solution

To solve the integral \[ I = \int_{0}^{\frac{\pi}{2}} e^x \frac{1 + \sin x}{1 + \cos x} \, dx, \] we can start by rewriting the integrand. The expression can be separated as follows: ...
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