What is the integral of (x+2)e^{2x} ?

The integral of (x+2)e^{2x} is 1/2 e^{2x}x+3/4 e^{2x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x+2)e^{2x}

\int (x + 2) e^{2 x} d x

\frac{1}{2} e^{2 x} x + \frac{3}{4} e^{2 x} + C

Solution steps

\int (x + 2) e^{2 x} d x

Apply Integration By Parts

= \frac{1}{2} e^{2 x} x + e^{2 x} - \int \frac{1}{2} e^{2 x} d x

\int \frac{1}{2} e^{2 x} d x = \frac{1}{4} e^{2 x}

= \frac{1}{2} e^{2 x} x + e^{2 x} - \frac{1}{4} e^{2 x}

Add similar elements:

e^{2 x} - \frac{1}{4} e^{2 x} = \frac{3}{4} e^{2 x}

= \frac{1}{2} e^{2 x} x + \frac{3}{4} e^{2 x}

Add a constant to the solution

= \frac{1}{2} e^{2 x} x + \frac{3}{4} e^{2 x} + C

What is the integral of (x+2)e^{2x} ?
The integral of (x+2)e^{2x} is 1/2 e^{2x}x+3/4 e^{2x}+C