integral of ex((1-x)/(1+x2))2 ?

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Grade 12Integral Calculus

integral of e^x((1-x)/(1+x²))²?

Siddharth Singh

12 Years agoGrade 12

1 Answer

Jitender Singh

12 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

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integral of ex((1-x)/(1+x2))2 ?

Siddharth Singh

1 Answer

Jitender Singh

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