What is the integral from 1 to 2 of x^3e^x ?

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

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integral from 1 to 2 of x^3e^x

\int_{1}^{2} x^{3} e^{x} d x

2 e^{2} + 2 e

Decimal Notation

20.21467 \dots

Solution steps

\int_{1}^{2} x^{3} e^{x} d x

Apply Integration By Parts

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

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

\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}))]_{1}^{2}

Compute the boundaries:

2 e^{2} + 2 e

= 2 e^{2} + 2 e

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