What is the integral of 4x^3e^x ?

The integral of 4x^3e^x is 4(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 4x^3e^x

\int 4 x^{3} e^{x} d x

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

Solution steps

\int 4 x^{3} e^{x} d x

Take the constant out:

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

= 4 \cdot \int x^{3} e^{x} d x

Apply Integration By Parts

= 4 (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}))

= 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x})))

Add a constant to the solution

= 4 (x^{3} e^{x} - 3 (x^{2} e^{x} - 2 (e^{x} x - e^{x}))) + C

What is the integral of 4x^3e^x ?
The integral of 4x^3e^x is 4(x^3e^x-3(x^2e^x-2(e^xx-e^x)))+C