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

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

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

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

arctan (x) + C

Solution steps

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

Cancel the common factor:

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