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

The integral from 0 to a of x^2e^x is a^2e^a-2(e^aa-e^a)-2

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

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

a^{2} e^{a} - 2 (e^{a} a - e^{a}) - 2

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

a^{2} e^{a} - 2 (e^{a} a - e^{a}) - 2

= a^{2} e^{a} - 2 (e^{a} a - e^{a}) - 2

\frac{\partial}{\partial x} (6 x^{3} y^{2})

x \to 1 lim ((5 x - 1)^{- 2})

\frac{d}{d x} ((4 x - 4) (3 x^{3} - x^{2} + 1))

y = \frac{1}{16 x ^{2}}, y = x, y = \frac{x}{18}

f (x) = sin (cos (4 x))

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