What is the integral from 0 to infinity of 6/(x^2+4) ?

The integral from 0 to infinity of 6/(x^2+4) is (3pi)/2

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integral from 0 to infinity of 6/(x^2+4)

\int_{0}^{\infty} \frac{6}{x ^{2} + 4} d x

\frac{3 π}{2}

Decimal

4.71238 \dots

Solution steps

\int_{0}^{\infty} \frac{6}{x ^{2} + 4} d x

Compute the indefinite integral:

\int \frac{6}{x ^{2} + 4} d x = 3 arctan (\frac{x}{2}) + C

Compute the boundaries:

\int_{0}^{\infty} \frac{6}{x ^{2} + 4} d x = 3 \cdot \frac{π}{2} - 0

= 3 \cdot \frac{π}{2} - 0

Simplify

= \frac{3 π}{2}

\int \frac{1}{x ^{2} 9 x ^{2} + 4} d x

\frac{d}{d x} ((6 x^{2} - 10 x) e^{x})

n = 1 \sum \infty e^{(2 n - 1)}

\int - 40 t^{\frac{2}{3}} d t

y = 7 e^{x} x

What is the integral from 0 to infinity of 6/(x^2+4) ?
The integral from 0 to infinity of 6/(x^2+4) is (3pi)/2