What is the integral from 0 to infinity of xe^{x^2} ?

The integral from 0 to infinity of xe^{x^2} is diverges

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integral from 0 to infinity of xe^{x^2}

\int_{0}^{\infty} x e^{x^{2}} d x

diverges

Solution steps

\int_{0}^{\infty} x e^{x^{2}} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} x e^{x^{2}} d x =

diverges

= diverges

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What is the integral from 0 to infinity of xe^{x^2} ?
The integral from 0 to infinity of xe^{x^2} is diverges