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

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

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

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

diverges

Solution steps

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

Compute the indefinite integral:

\int \frac{x}{x ^{2} + 4} d x = \frac{1}{2} ln x^{2} + 4 + C

Compute the boundaries:

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

diverges

= diverges

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\int_{0}^{\frac{1}{3}} x 1 - 5 x^{2} d x

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