What is the integral from 0 to infinity of 5/(x^2+6) ?

The integral from 0 to infinity of 5/(x^2+6) is (5pi)/(2sqrt(6))

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integral from 0 to infinity of 5/(x^2+6)

\int_{0}^{\infty} \frac{5}{x ^{2} + 6} d x

\frac{5 π}{2 6}

Decimal

3.20637 \dots

Solution steps

\int_{0}^{\infty} \frac{5}{x ^{2} + 6} d x

Compute the indefinite integral:

\int \frac{5}{x ^{2} + 6} d x = \frac{5}{6} arctan (\frac{x}{6}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{5}{x ^{2} + 6} d x = \frac{5}{6} \cdot \frac{π}{2} - 0

= \frac{5}{6} \cdot \frac{π}{2} - 0

Simplify

= \frac{5 π}{2 6}

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What is the integral from 0 to infinity of 5/(x^2+6) ?
The integral from 0 to infinity of 5/(x^2+6) is (5pi)/(2sqrt(6))