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

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

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

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

diverges

Solution steps

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

Compute the indefinite integral:

\int x e^{4 x} d x = \frac{1}{16} (e^{4 x} \cdot 4 x - e^{4 x}) + C

Compute the boundaries:

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

diverges

= diverges

2^{\frac{1}{x}}

\int \frac{3 x ^{2}}{( 25 + x ^{2} ) ^{2}} d x

\int sin^{10} (x) cos^{3} (x) d x

\int sin^{3} (2 x) cos^{2} (2 x) d x

x \to 1 lim (\frac{( sin ( x ) )}{x})

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