What is the integral of 15x^3e^x ?

The integral of 15x^3e^x is 15(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C

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integral of 15x^3e^x

\int 15 x^{3} e^{x} d x

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

Solution steps

\int 15 x^{3} e^{x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 15 \cdot \int x^{3} e^{x} d x

Apply Integration By Parts

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

= 15 (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}))

= 15 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

Add a constant to the solution

= 15 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

x \to \infty lim (- x)

\frac{d}{d x} (8 x arcsin (x))

\frac{d}{d x} (3 x ln (9 x^{2}))

x \to 0 lim (e^{(\frac{1}{x})})

\int (1 + (\frac{1}{2}) \cdot \frac{2}{( 2 \cdot x + 3 )}) d x

What is the integral of 15x^3e^x ?
The integral of 15x^3e^x is 15(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C