What is the integral of (5/(x^2+1)) ?

The integral of (5/(x^2+1)) is 5arctan(x)+C

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integral of (5/(x^2+1))

\int (\frac{5}{x ^{2} + 1}) d x

5 arctan (x) + C

Solution steps

\int \frac{5}{x ^{2} + 1} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 5 \cdot \int \frac{1}{x ^{2} + 1} d x

Use the common integral:

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

= 5 arctan (x)

Add a constant to the solution

= 5 arctan (x) + C

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What is the integral of (5/(x^2+1)) ?
The integral of (5/(x^2+1)) is 5arctan(x)+C