What is the integral from 0 to 5 of x^2e^x ?

The integral from 0 to 5 of x^2e^x is 17e^5-2

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integral from 0 to 5 of x^2e^x

\int_{0}^{5} x^{2} e^{x} d x

17 e^{5} - 2

Decimal

2521.02370 \dots

Solution steps

\int_{0}^{5} x^{2} e^{x} d x

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{5}

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{5}

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

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{5}

Compute the boundaries:

17 e^{5} - 2

= 17 e^{5} - 2

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\int_{- 2}^{2} 3 x^{3} - x^{2} + 5 x - 4 d x

What is the integral from 0 to 5 of x^2e^x ?
The integral from 0 to 5 of x^2e^x is 17e^5-2