What is the integral from 1 to 2 of x^2e^x ?

The integral from 1 to 2 of x^2e^x is 2e^2-e

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integral from 1 to 2 of x^2e^x

\int_{1}^{2} x^{2} e^{x} d x

2 e^{2} - e

Decimal

12.05983 \dots

Solution steps

\int_{1}^{2} x^{2} e^{x} d x

Apply Integration By Parts

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{1}^{2}

\int 2 x e^{x} d x = 2 (e^{x} x - e^{x})

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{1}^{2}

Compute the boundaries:

2 e^{2} - e

= 2 e^{2} - e

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What is the integral from 1 to 2 of x^2e^x ?
The integral from 1 to 2 of x^2e^x is 2e^2-e