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Integrate the function e^x((1+sinx)/(1+c...

Integrate the function `e^x((1+sinx)/(1+cosx))`

Text Solution

Verified by Experts

the above integral becomes
`I=int(e^x(sec^2(x/2)/2+tan(x/2))`
THis is the standard form
`int(e^xf(x)+f'(x))`
thus,
`f(x)=tan(x/2)`
Thus, the integral is solved as
`I=e^xtan(x/2)+C`
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