What is the integral of (x^2-2x+1)/((x-1)^2*(x^2+1)) ?

The integral of (x^2-2x+1)/((x-1)^2*(x^2+1)) is arctan(x)+C

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integral of (x^2-2x+1)/((x-1)^2*(x^2+1))

\int \frac{x ^{2} - 2 x + 1}{( x - 1 ) ^{2} \cdot ( x ^{2} + 1 )} d x

arctan (x) + C

Solution steps

\int \frac{x ^{2} - 2 x + 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} d x

Simplify

\frac{x ^{2} - 2 x + 1}{( x - 1 ) ^{2} ( x ^{2} + 1 )} : \frac{1}{x ^{2} + 1}

= \int \frac{1}{x ^{2} + 1} d x

Use the common integral:

\int \frac{1}{x ^{2} + 1} d x = arctan (x)

= arctan (x)

Add a constant to the solution

= arctan (x) + C

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What is the integral of (x^2-2x+1)/((x-1)^2*(x^2+1)) ?
The integral of (x^2-2x+1)/((x-1)^2*(x^2+1)) is arctan(x)+C