What is the integral from 0 to infinity of (x-1)e^x ?

The integral from 0 to infinity of (x-1)e^x is diverges

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integral from 0 to infinity of (x-1)e^x

\int_{0}^{\infty} (x - 1) e^{x} d x

diverges

Solution steps

\int_{0}^{\infty} (x - 1) e^{x} d x

Compute the indefinite integral:

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

Compute the boundaries:

\int_{0}^{\infty} (x - 1) e^{x} d x =

diverges

= diverges

What is the integral from 0 to infinity of (x-1)e^x ?
The integral from 0 to infinity of (x-1)e^x is diverges