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

The integral from-1 to 1 of x^2e^x is e-5/e

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

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

e - \frac{5}{e}

Decimal Notation

0.87888 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

e - \frac{5}{e}

= e - \frac{5}{e}

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What is the integral from-1 to 1 of x^2e^x ?
The integral from-1 to 1 of x^2e^x is e-5/e