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Evaluate: inte^x\ ((1+sinx)/(1+cosx))\ d...

Evaluate: `inte^x\ ((1+sinx)/(1+cosx))\ dx`

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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