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Find int(e^x(1+x))/(sin^2(x e^x))dx...

Find `int(e^x(1+x))/(sin^2(x e^x))dx`

Text Solution

Verified by Experts

Let `z=xe^(x). " Then " dz=(1e^(x)+xe^(x))dx=e^(x)(1+x)dx`. Thus,
`int(e^(x)(1+x))/(cos^(2)(xe^(x)))dx=int(dx)/(cos^(2)z)`
`=int sec^(2)zdz`
`=tan z+c=tan(xe^(x))+c`
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