What is the integral from-infinity to 0 of 3/(9+x^2) ?

The integral from-infinity to 0 of 3/(9+x^2) is pi/2

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integral from-infinity to 0 of 3/(9+x^2)

\int_{- \infty}^{0} \frac{3}{9 + x ^{2}} d x

\frac{π}{2}

Decimal Notation

1.57079 \dots

Solution steps

\int_{- \infty}^{0} \frac{3}{9 + x ^{2}} d x

Compute the indefinite integral:

\int \frac{3}{9 + x ^{2}} d x = arctan (\frac{x}{3}) + C

Compute the boundaries:

\int_{- \infty}^{0} \frac{3}{9 + x ^{2}} d x = 0 - (- \frac{π}{2})

= 0 - (- \frac{π}{2})

Simplify

= \frac{π}{2}

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What is the integral from-infinity to 0 of 3/(9+x^2) ?
The integral from-infinity to 0 of 3/(9+x^2) is pi/2