What is the integral from 0 to ln(5) of xe^x ?

The integral from 0 to ln(5) of xe^x is 5ln(5)-4

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integral from 0 to ln(5) of xe^x

\int_{0}^{l n (5)} x e^{x} d x

5 ln (5) - 4

Decimal

4.04718 \dots

Solution steps

\int_{0}^{l n (5)} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{0}^{l n (5)}

= [e^{x} x - \int e^{x} d x]_{0}^{l n (5)}

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

= [e^{x} x - e^{x}]_{0}^{l n (5)}

Compute the boundaries:

5 ln (5) - 4

= 5 ln (5) - 4

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What is the integral from 0 to ln(5) of xe^x ?
The integral from 0 to ln(5) of xe^x is 5ln(5)-4