What is the integral from 3 to infinity of 7/(x^2+2) ?

The integral from 3 to infinity of 7/(x^2+2) is (7pi-14arctan((3sqrt(2))/2))/(2sqrt(2))

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integral from 3 to infinity of 7/(x^2+2)

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x

\frac{7 π - 14 arctan ( \frac{3 2}{2} )}{2 2}

Decimal Notation

2.18041 \dots

Solution steps

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x

Compute the indefinite integral:

\int \frac{7}{x ^{2} + 2} d x = \frac{7}{2} arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{3}^{\infty} \frac{7}{x ^{2} + 2} d x = \frac{7}{2} \cdot \frac{π}{2} - \frac{7}{2} arctan (\frac{3}{2})

= \frac{7}{2} \cdot \frac{π}{2} - \frac{7}{2} arctan (\frac{3}{2})

Simplify

= \frac{7 π - 14 arctan ( \frac{3 2}{2} )}{2 2}

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What is the integral from 3 to infinity of 7/(x^2+2) ?
The integral from 3 to infinity of 7/(x^2+2) is (7pi-14arctan((3sqrt(2))/2))/(2sqrt(2))