What is the integral from 1 to 4 of x^3e^x ?

The integral from 1 to 4 of x^3e^x is 34e^4+2e

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integral from 1 to 4 of x^3e^x

\int_{1}^{4} x^{3} e^{x} d x

34 e^{4} + 2 e

Decimal Notation

1861.77366 \dots

Solution steps

\int_{1}^{4} x^{3} e^{x} d x

Apply Integration By Parts

: [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{1}^{4}

= [x^{3} e^{x} - \int 3 x^{2} e^{x} d x]_{1}^{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}))]_{1}^{4}

Compute the boundaries:

34 e^{4} + 2 e

= 34 e^{4} + 2 e

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What is the integral from 1 to 4 of x^3e^x ?
The integral from 1 to 4 of x^3e^x is 34e^4+2e