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Evaluate: int1/((x+1)^2(x^2+1))\ dx...

Evaluate: `int1/((x+1)^2(x^2+1))\ dx`

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