What is the integral from 0 to 5 of x^3e^x ?

The integral from 0 to 5 of x^3e^x is 74e^5+6

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integral from 0 to 5 of x^3e^x

\int_{0}^{5} x^{3} e^{x} d x

74 e^{5} + 6

Decimal Notation

10988.57377 \dots

Solution steps

\int_{0}^{5} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{5}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{5}

\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}^{5}

Compute the boundaries:

74 e^{5} + 6

= 74 e^{5} + 6

y^{^{''}} + 121 y = cos (8 t)

\int \frac{7}{x ^{2} - 9} d x

\frac{\partial}{\partial y} (4 x^{2} - y^{2} + 2 y)

\int cos (6 x) cos (4 x) d x

x (x - 9)^{2}

What is the integral from 0 to 5 of x^3e^x ?
The integral from 0 to 5 of x^3e^x is 74e^5+6