What is the integral from 0 to 1 of x^3e^x ?

The integral from 0 to 1 of x^3e^x is -2e+6

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integral from 0 to 1 of x^3e^x

\int_{0}^{1} x^{3} e^{x} d x

- 2 e + 6

Decimal

0.56343 \dots

Solution steps

\int_{0}^{1} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{1}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{0}^{1}

\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}^{1}

Compute the boundaries:

- 2 e + 6

= - 2 e + 6

x \to 25 lim (2 x + 2 x)

\int - 9 cos (x) d x

x \to 3 lim (\frac{x - 1}{x ^{2} - 2})

\frac{d}{d x} (x^{6} + x)

x y^{2} d x = d y - x d x

What is the integral from 0 to 1 of x^3e^x ?
The integral from 0 to 1 of x^3e^x is -2e+6