What is the integral from 0 to 4 of x^2e^x ?

The integral from 0 to 4 of x^2e^x is 10e^4-2

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integral from 0 to 4 of x^2e^x

\int_{0}^{4} x^{2} e^{x} d x

10 e^{4} - 2

Decimal

543.98150 \dots

Solution steps

\int_{0}^{4} x^{2} e^{x} d x

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{4}

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{4}

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

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{4}

Compute the boundaries:

10 e^{4} - 2

= 10 e^{4} - 2

\int_{- 4}^{4} - e^{(\frac{1}{4}) x} d x

\int_{4}^{8} 10 - x d x

\int_{0}^{2} 4 x^{2} + 1 d x

\int_{- 2}^{0} 4 x - x^{2} - 6 x d x

\int_{1}^{4} \frac{x - 9}{x} d x

What is the integral from 0 to 4 of x^2e^x ?
The integral from 0 to 4 of x^2e^x is 10e^4-2