What is the integral from-infinity to 0 of 1/(x^2+1) ?

The integral from-infinity to 0 of 1/(x^2+1) is pi/2

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integral from-infinity to 0 of 1/(x^2+1)

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{- \infty}^{0} \frac{1}{x ^{2} + 1} d x = 0 - (- \frac{π}{2})

= 0 - (- \frac{π}{2})

Simplify

= \frac{π}{2}

What is the integral from-infinity to 0 of 1/(x^2+1) ?
The integral from-infinity to 0 of 1/(x^2+1) is pi/2