What is the integral from 0 to 3 of (x^2e^x) ?

The integral from 0 to 3 of (x^2e^x) is 5e^3-2

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integral from 0 to 3 of (x^2e^x)

\int_{0}^{3} (x^{2} e^{x}) d x

5 e^{3} - 2

Decimal

98.42768 \dots

Solution steps

\int_{0}^{3} x^{2} e^{x} d x

Apply Integration By Parts

: [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{3}

= [x^{2} e^{x} - \int 2 x e^{x} d x]_{0}^{3}

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

= [x^{2} e^{x} - 2 (e^{x} x - e^{x})]_{0}^{3}

Compute the boundaries:

5 e^{3} - 2

= 5 e^{3} - 2

\int_{- 2}^{0} (x^{3} - 3 x^{2} - 10 x) d x

\int_{- 1}^{0} arccos (x) d x

\int_{0.25}^{0.6} 5 (1 - x)^{4} d x

\int_{- 3}^{0} x^{3} + 5 x^{2} + 6 x d x

\int_{0}^{0.4} \frac{1}{1 + x ^{4}} d x

What is the integral from 0 to 3 of (x^2e^x) ?
The integral from 0 to 3 of (x^2e^x) is 5e^3-2