What is the integral of e^xx^3 ?

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

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integral of e^xx^3

\int e^{x} 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

\int_{3}^{6} \frac{1}{3 x + 7} d x

\frac{d}{d x} ((3 x^{4}) (4 x^{3} + 4 x))

\int \frac{e ^{2 x}}{e ^{x} - 5} d x

f (x) = (7 x^{2} - 12 x) e^{x}

3 x^{2}, x^{2} + 6

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