What is the integral of e^x*x^3 ?

The integral of e^x*x^3 is x^3e^x-3(x^2e^x-2(e^xx-e^x))+C

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integral of e^x*x^3

\int e^{x} \cdot x^{3} d x

x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

Solution steps

\int e^{x} x^{3} d x

Apply Integration By Parts

: x^{3} e^{x} - \int 3 x^{2} e^{x} d x

= x^{3} e^{x} - \int 3 x^{2} e^{x} d x

\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}))

Add a constant to the solution

= x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})) + C

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 t e^{2 t}

\int ln (x) \frac{1}{x} d x

(5 x^{6} + 4 x^{3})^{4}

\frac{d}{d x} (x + \frac{16}{x})

What is the integral of e^x*x^3 ?
The integral of e^x*x^3 is x^3e^x-3(x^2e^x-2(e^xx-e^x))+C