What is the integral of (4x+5)e^x ?

The integral of (4x+5)e^x is 4e^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+5)e^x

\int (4 x + 5) e^{x} d x

4 e^{x} x + e^{x} + C

Solution steps

\int (4 x + 5) e^{x} d x

Apply Integration By Parts

= (4 x + 5) e^{x} - \int 4 e^{x} d x

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

= (4 x + 5) e^{x} - 4 e^{x}

Simplify

(4 x + 5) e^{x} - 4 e^{x} : 4 e^{x} x + e^{x}

= 4 e^{x} x + e^{x}

Add a constant to the solution

= 4 e^{x} x + e^{x} + C