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

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

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integral from 0 to 3 of x^2*e^x

\int_{0}^{3} x^{2} \cdot 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_{3}^{x^{4}} sin (5 t) t^{5} d t

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

\int_{1}^{2} 5 - 2 x d x

\int_{0}^{π} x \cdot cos (3 x) d x

\int_{- 1}^{1} \frac{1}{e ^{x}} d x

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