What is the integral of 13x^3e^x ?

The integral of 13x^3e^x is 13(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C

Popular >

integral of 13x^3e^x

\int 13 x^{3} e^{x} d x

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

Solution steps

\int 13 x^{3} e^{x} d x

Take the constant out:

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

= 13 \cdot \int x^{3} e^{x} d x

Apply Integration By Parts

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

= 13 (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}))

= 13 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

Add a constant to the solution

= 13 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

\frac{( x + 1 )}{x + 5}

\int \frac{5 x ^{2} + 3 x + 5}{( x ^{2} + 1 ) ^{2}} d x

\frac{\partial}{\partial x} (12 x + 2 y - 3 x^{2} - y^{2})

x + 7, 0.5 (x + 7), - 7, - 3

(8, 1230), (16, 2430)

What is the integral of 13x^3e^x ?
The integral of 13x^3e^x is 13(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C