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

The integral from 0 to 2 of x^3e^x is 2e^2+6

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

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

2 e^{2} + 6

Solution steps

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

Apply Integration By Parts

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

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

\int 3 x^{2} e^{x} d x = 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))

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

Compute the boundaries:

2 e^{2} + 6

= 2 e^{2} + 6

x \to 4 - lim (\frac{x - 9}{x - 4})

y^{^{'}} = a - b y

\int t 1 + t t d t

f (x) = 1 - 10 x, at x = - 1

\int (- 1)^{n} x^{2 n} d x

What is the integral from 0 to 2 of x^3e^x ?
The integral from 0 to 2 of x^3e^x is 2e^2+6