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integral of e x ((1-x)/(1+x 2 )) 2 ?

integral of ex((1-x)/(1+x2))?

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
\int \frac{e^{x}(1-x)^{2}}{(1+x^{2})^{2}}dx = \frac{e^{x}}{x^{2}+1} + constant
I = \int \frac{e^{x}(1-x)^{2}}{(1+x^{2})^{2}}dx
I = \int \frac{e^{x}(x^{2}-2x+1)}{(1+x^{2})^{2}}dx
I = \int [\frac{e^{x}}{x^{2}+1}-\frac{2x.e^{x}}{x^{2}+1}]dx
I = \int (\frac{e^{x}}{x^{2}+1})^{'}dx
I = \frac{e^{x}}{x^{2}+1} + constant
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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