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

The integral of e^x*x^3 is 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 e^x*x^3

integral

e^{x} \cdot x^{3}

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

Solution steps

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

Apply Integration By Parts

= 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

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