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Evaluate: int3/((1-x)(1+x^2))\ dx...

Evaluate: `int3/((1-x)(1+x^2))\ dx`

Text Solution

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`I=int frac{3 d x}{(1-x)(1+x^{2})}`
`=3 int frac{d x}{(1-x)(1+x^{2})}`
Let `frac{1}{(1-x)(1+x^{2})}=frac{A}{1-x}+frac{B x+C}{x^{2}+1}`
`Rightarrow frac{1}{(1-x)(x^{2}+1)}=frac{A(x^{2}+1)+(B x+C)(1-x)}{(1-x)(x^{2}+1)}`
`Rightarrow 1=A x^{2}+A+B x-B x^{2}+C-C x` `Rightarrow 1=(A-B) x^{2}+(B-C) x+A+C`
Equating coefficients of like terms.
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