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

The integral from 3 to infinity of 2/(x^2+9) is pi/6

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

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

\frac{π}{6}

Decimal

0.52359 \dots

Solution steps

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

Compute the indefinite integral:

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

Compute the boundaries:

\int_{3}^{\infty} \frac{2}{x ^{2} + 9} d x = \frac{π}{3} - \frac{π}{6}

= \frac{π}{3} - \frac{π}{6}

Simplify

= \frac{π}{6}

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What is the integral from 3 to infinity of 2/(x^2+9) ?
The integral from 3 to infinity of 2/(x^2+9) is pi/6