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प्रश्न
Integrate the function in `(xe^x)/(1+x)^2`.
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उत्तर
Let `I = int (xe^x)/((1 + x)^2) dx`
`= int ((x + 1 - 1) e^x)/((1 + x)^2) dx`
`= int 1/((1 + x)) . e^x dx - (e^x - 1)/((1 + x)^2) dx`
`= 1/((1 + x)). e^x - int (-1)/((1 + x^2)).e^x dx - int e^x/((1 + x^2)) dx + C`
`= e^x/(1 + x) + int e^x/((1 + x)^2) dx - int e^x/((1 + x)^2) dx + C`
`= e^x/(1 + x) + C`
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