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Solve any one of the following.
Evaluate: ∫ (dx)/((x-1)²(x² + 1)²)
Evaluate: $\int \frac{dx}{(x-1)^2(x^2 + 1)^2}$
Answer
Answer
Integral: $\int \left(1/((x-1)^2 (x^2+1)^2)\right) dx$
Use partial fractions in the form $\frac{1}{(x-1)^2(x^2+1)^2}=\frac{A}{x-1}+\frac{B}{(x-1)^2}+\frac{Cx+D}{x^2+1}+\frac{Ex+F}{(x^2+1)^2}$ and integrate each term.
Final answer: $-\frac{x(x+1)}{4(x-1)(x^2+1)}-\frac12\log|x-1|+\frac14\log(x^2+1)+\frac14\tan^{-1}x+C$