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

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

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integral of 1/(n^2+1)

\int \frac{1}{n ^{2} + 1}

\frac{x}{n ^{2} + 1} + C

Solution steps

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

Integral of a constant:

\int a d x = a x

= \frac{1}{n ^{2} + 1} x

Simplify

\frac{1}{n ^{2} + 1} x : \frac{x}{n ^{2} + 1}

= \frac{x}{n ^{2} + 1}

Add a constant to the solution

= \frac{x}{n ^{2} + 1} + C