What is the integral from 0 to 2 of e^xx^3 ?

The integral from 0 to 2 of e^xx^3 is 2e^2+6

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integral from 0 to 2 of e^xx^3

\int_{0}^{2} e^{x} x^{3} d x

2 e^{2} + 6

Decimal Notation

20.77811 \dots

Solution steps

\int_{0}^{2} e^{x} x^{3} d x

Apply Integration By Parts

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

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

Compute the boundaries:

2 e^{2} + 6

= 2 e^{2} + 6

\int_{0}^{4} ln (1 + x) d x

\int_{0}^{5} x (5 - x) d x

\int_{\infty}^{0} x e^{- 4 x} d x

\int_{2}^{4} 2 + x d x

\int_{0}^{4} 12 d x

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