What is the integral from 0 to 8 of x^3e^x ?

The integral from 0 to 8 of x^3e^x is 362e^8+6

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integral from 0 to 8 of x^3e^x

\int_{0}^{8} x^{3} e^{x} d x

362 e^{8} + 6

Decimal

1079112.79130 \dots

Solution steps

\int_{0}^{8} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{8}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{8}

\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}^{8}

Compute the boundaries:

362 e^{8} + 6

= 362 e^{8} + 6

f (x) = 3 x^{\frac{1}{2}} + x^{- \frac{3}{2}}

\frac{x - 4}{x + 4}

y = x^{2} - 6 x + 9, (3, 0)

x \to \infty lim (x^{2} - 2 x)

\int \frac{1}{( x + 1 ) ( x + 2 )} d x

What is the integral from 0 to 8 of x^3e^x ?
The integral from 0 to 8 of x^3e^x is 362e^8+6