What is the integral from 0 to infinity of 4xe^{ax} ?

The integral from 0 to infinity of 4xe^{ax} is diverges

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integral from 0 to infinity of 4xe^{ax}

\int_{0}^{\infty} 4 x e^{a x} d x

diverges

Solution steps

\int_{0}^{\infty} 4 x e^{a x} d x

Compute the indefinite integral:

\int 4 x e^{a x} d x = 4 (e^{a x} \frac{1}{a} x - e^{a x} \frac{1}{a ^{2}}) + C

Compute the boundaries:

\int_{0}^{\infty} 4 x e^{a x} d x =

diverges

= diverges

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What is the integral from 0 to infinity of 4xe^{ax} ?
The integral from 0 to infinity of 4xe^{ax} is diverges