What is the integral of e^xx^4 ?

The integral of e^xx^4 is x^4e^x-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 e^xx^4

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

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

Solution steps

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

Apply Integration By Parts

= x^{4} e^{x} - \int 4 x^{3} e^{x} d 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})))

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

Add a constant to the solution

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

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