What is the integral from 0 to 4 of x^3e^x ?

The integral from 0 to 4 of x^3e^x is 34e^4+6

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integral from 0 to 4 of x^3e^x

\int_{0}^{4} x^{3} e^{x} d x

34 e^{4} + 6

Decimal Notation

1862.33710 \dots

Solution steps

\int_{0}^{4} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{4}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{4}

\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}^{4}

Compute the boundaries:

34 e^{4} + 6

= 34 e^{4} + 6

x, 2 x - 12, 0, 8

\frac{d}{d x} (\frac{1}{8} x)

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

x \to \infty lim (\frac{x}{- 1})

6 e^{3 x} (3 cos (4 x) - 4 sin (4 x))

What is the integral from 0 to 4 of x^3e^x ?
The integral from 0 to 4 of x^3e^x is 34e^4+6