What is the integral from 2 to 3 of xe^x ?

The integral from 2 to 3 of xe^x is 2e^3-e^2

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integral from 2 to 3 of xe^x

\int_{2}^{3} x e^{x} d x

2 e^{3} - e^{2}

Decimal

32.78201 \dots

Solution steps

\int_{2}^{3} x e^{x} d x

Apply Integration By Parts

: [e^{x} x - \int e^{x} d x]_{2}^{3}

= [e^{x} x - \int e^{x} d x]_{2}^{3}

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

= [e^{x} x - e^{x}]_{2}^{3}

Compute the boundaries:

2 e^{3} - e^{2}

= 2 e^{3} - e^{2}

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\int_{1}^{e} \frac{1}{x ( 1 + ln ^{2} ( x ) )} d x

What is the integral from 2 to 3 of xe^x ?
The integral from 2 to 3 of xe^x is 2e^3-e^2