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

The integral from 1 to 5 of 1/(x^2+1) is arctan(5)-pi/4

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

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

arctan (5) - \frac{π}{4}

Decimal

0.58800 \dots

Solution steps

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

Use the common integral:

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

= [arctan (x)]_{1}^{5}

Compute the boundaries:

arctan (5) - \frac{π}{4}

= arctan (5) - \frac{π}{4}

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What is the integral from 1 to 5 of 1/(x^2+1) ?
The integral from 1 to 5 of 1/(x^2+1) is arctan(5)-pi/4