What is the integral from 0 to ln(20) of xe^x ?

The integral from 0 to ln(20) of xe^x is 20ln(20)-19

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integral from 0 to ln(20) of xe^x

\int_{0}^{l n (20)} x e^{x} d x

20 ln (20) - 19

Decimal

40.91464 \dots

Solution steps

\int_{0}^{l n (20)} x e^{x} d x

Apply Integration By Parts

= [e^{x} x - \int e^{x} d x]_{0}^{l n (20)}

\int e^{x} d x = e^{x}

= [e^{x} x - e^{x}]_{0}^{l n (20)}

Compute the boundaries:

20 ln (20) - 19

= 20 ln (20) - 19

What is the integral from 0 to ln(20) of xe^x ?
The integral from 0 to ln(20) of xe^x is 20ln(20)-19