What is the integral from 0 to infinity of 6xe^{3x} ?

The integral from 0 to infinity of 6xe^{3x} is diverges

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integral from 0 to infinity of 6xe^{3x}

\int_{0}^{\infty} 6 x e^{3 x} d x

diverges

Solution steps

\int_{0}^{\infty} 6 x e^{3 x} d x

Compute the indefinite integral:

\int 6 x e^{3 x} d x = 2 e^{3 x} x - \frac{2}{3} e^{3 x} + C

Compute the boundaries:

\int_{0}^{\infty} 6 x e^{3 x} d x =

diverges

= diverges

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What is the integral from 0 to infinity of 6xe^{3x} ?
The integral from 0 to infinity of 6xe^{3x} is diverges