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Integrate the following functions e^x((1...

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

Text Solution

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`int e^x((1+sinx)/(1+cosx)) dx`
=`int e^x((1+2sin (x/2) cos(x/2)/(2cos^2 (x/2)) dx`
=`int e^x(1/2 sec^2 (x/2) + tan (x/2)) dx`
=`e^x tan(x/2)+c, f(x) = tan x/2`
`f^.(x) = 1/2 sec^2 x/2`
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