What is the integral from 0 to ln(10) of xe^x ?

The integral from 0 to ln(10) of xe^x is 10ln(10)-9

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integral from 0 to ln(10) of xe^x

\int_{0}^{l n (10)} x e^{x} d x

10 ln (10) - 9

Decimal Notation

14.02585 \dots

Solution steps

\int_{0}^{l n (10)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{l n (10)}

= [e^{x} x - \int e^{x} d x]_{0}^{l n (10)}

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

= [e^{x} x - e^{x}]_{0}^{l n (10)}

Compute the boundaries:

10 ln (10) - 9

= 10 ln (10) - 9

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What is the integral from 0 to ln(10) of xe^x ?
The integral from 0 to ln(10) of xe^x is 10ln(10)-9