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Q17  Integrate the functions \frac{x e ^x }{( 1+ x )^2}

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\frac{x e ^x }{( 1+ x )^2}
Let suppose 
I = \int \frac{e^x(x)}{(1+x)^2}dx
by rearranging the equation, we get
\Rightarrow \int e^x[\frac{1}{1+x}-\frac{1}{(1+x)^2}]dx
let
 f(x)=\frac{1}{1+x} \Rightarrow f'(x)= -\frac{1}{(1+x)^2}
It is known that \int e^x[f(x)+f'(x)]=e^x[f(x)]+C
therefore the solution of the given integral is 

I = \frac{e^x}{1+x}+C

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manish

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