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

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

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

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

\frac{π}{2} - arctan (2)

Decimal

0.46364 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

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

= \frac{π}{2} - arctan (2)

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