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

The integral from 0 to ln(4) of xe^x is 8ln(2)-3

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integral from 0 to ln(4) of xe^x

\int_{0}^{l n (4)} x e^{x} d x

8 ln (2) - 3

Decimal

2.54517 \dots

Solution steps

\int_{0}^{l n (4)} x e^{x} d x

Apply Integration By Parts

= [e^{x} x - \int e^{x} d x]_{0}^{2 l n (2)}

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

= [e^{x} x - e^{x}]_{0}^{2 l n (2)}

Compute the boundaries:

8 ln (2) - 3

= 8 ln (2) - 3

What is the integral from 0 to ln(4) of xe^x ?
The integral from 0 to ln(4) of xe^x is 8ln(2)-3