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

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

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integral of x^3*e^x

integral

x^{3} \cdot e^{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

\frac{x}{( x ^{2} - 2 x + 2 )}

\frac{1}{( 1 + \frac{1}{2} x )}

\frac{cos ^{23} ( x )}{sin ( x )}

\frac{2}{( x ^{2} + 2 )}

2 x (1 - x^{- 3})

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