What is the integral from s to infinity of 1/(s^2+1) ?

The integral from s to infinity of 1/(s^2+1) is pi/2-arctan(s)

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integral from s to infinity of 1/(s^2+1)

\int_{s}^{\infty} \frac{1}{s ^{2} + 1} d s

\frac{π}{2} - arctan (s)

Solution steps

\int_{s}^{\infty} \frac{1}{s ^{2} + 1} d s

Compute the indefinite integral:

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

Compute the boundaries:

\int_{s}^{\infty} \frac{1}{s ^{2} + 1} d s = \frac{π}{2} - arctan (s)

= \frac{π}{2} - arctan (s)

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What is the integral from s to infinity of 1/(s^2+1) ?
The integral from s to infinity of 1/(s^2+1) is pi/2-arctan(s)