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

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

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integral of x^3e^x

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

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

Solution steps

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

(x^{3} + y^{3}) d x + 3 x y^{2} d y = 0

\frac{d}{d x} ((8 x + 7)^{2})

\int \frac{1}{cos ( 3 x )} d x

- 9 x^{\frac{1}{2}} + x^{\frac{3}{2}}

(4, - 8), (8, 5)

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