What is the integral from 1 to 3 of x^2e^x ?

The integral from 1 to 3 of x^2e^x is 5e^3-e

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integral from 1 to 3 of x^2e^x

\int_{1}^{3} x^{2} e^{x} d x

5 e^{3} - e

Solution steps

\int_{1}^{3} x^{2} e^{x} d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

5 e^{3} - e

= 5 e^{3} - e

f (x) = x^{2}, at x = - \frac{1}{4}

y^{^{'}} - 2 x y - 8 = 0

e^{3 (t + 1)}

y = x (3 x - 2)^{4}

What is the integral from 1 to 3 of x^2e^x ?
The integral from 1 to 3 of x^2e^x is 5e^3-e