What is the integral from 0 to 7 of x^3e^x ?

The integral from 0 to 7 of x^3e^x is 232e^7+6

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integral from 0 to 7 of x^3e^x

\int_{0}^{7} x^{3} e^{x} d x

232 e^{7} + 6

Decimal Notation

254424.89275 \dots

Solution steps

\int_{0}^{7} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{7}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{7}

\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}^{7}

Compute the boundaries:

232 e^{7} + 6

= 232 e^{7} + 6

f (x) = \frac{1}{4 x ^{\frac{3}{2}}}, at x = 4

\frac{d y}{d x} = 6 x^{2} y

\int e^{r^{2}} d r

x \to 0 lim (\frac{ln ( 1 )}{x})

\int (x^{7} - 2 x^{6})^{5} (7 x^{6} - 12 x^{5}) d x

What is the integral from 0 to 7 of x^3e^x ?
The integral from 0 to 7 of x^3e^x is 232e^7+6