What is the integral from-1 to 1 of x^3e^x ?

The integral from-1 to 1 of x^3e^x is -2e+(16)/e

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integral from-1 to 1 of x^3e^x

\int_{- 1}^{1} x^{3} e^{x} d x

- 2 e + \frac{16}{e}

Decimal

0.44950 \dots

Solution steps

\int_{- 1}^{1} x^{3} e^{x} d x

Apply Integration By Parts

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{- 1}^{1}

\int 3 x^{2} e^{x} d x = 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

= [x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))]_{- 1}^{1}

Compute the boundaries:

- 2 e + \frac{16}{e}

= - 2 e + \frac{16}{e}

What is the integral from-1 to 1 of x^3e^x ?
The integral from-1 to 1 of x^3e^x is -2e+(16)/e