What is the integral of (2x-1)e^x ?

The integral of (2x-1)e^x is 2e^xx-3e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x-1)e^x

\int (2 x - 1) e^{x} d x

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

Solution steps

\int (2 x - 1) e^{x} d x

Apply Integration By Parts

= (2 x - 1) e^{x} - \int 2 e^{x} d x

\int 2 e^{x} d x = 2 e^{x}

= (2 x - 1) e^{x} - 2 e^{x}

Simplify

(2 x - 1) e^{x} - 2 e^{x} : 2 e^{x} x - 3 e^{x}

= 2 e^{x} x - 3 e^{x}

Add a constant to the solution

= 2 e^{x} x - 3 e^{x} + C