What is the integral from 0 to infinity of x*e^x ?

The integral from 0 to infinity of x*e^x is diverges

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integral from 0 to infinity of x*e^x

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

diverges

Solution steps

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

Compute the indefinite integral:

\int x e^{x} d x = e^{x} x - e^{x} + C

Compute the boundaries:

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

diverges

= diverges

\int_{0}^{π} x sin (k x) d x

\int_{0}^{y} \frac{2 x ^{2}}{y ^{2}} d x

\int_{\frac{1}{6}}^{e} ∣ ln (x) ∣ d x

\int_{0}^{2 π} cos (x) + 1 d x

\int_{0}^{y} x \cdot \frac{2 x}{y ^{2}} d x

What is the integral from 0 to infinity of x*e^x ?
The integral from 0 to infinity of x*e^x is diverges