What is the integral of (2x-3)e^x ?

The integral of (2x-3)e^x is 2e^xx-5e^x+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x-3)e^x

\int (2 x - 3) e^{x} d x

2 e^{x} x - 5 e^{x} + C

Solution steps

\int (2 x - 3) e^{x} d x

Apply Integration By Parts

= (2 x - 3) e^{x} - \int 2 e^{x} d x

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

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

Simplify

(2 x - 3) e^{x} - 2 e^{x} : 2 e^{x} x - 5 e^{x}

= 2 e^{x} x - 5 e^{x}

Add a constant to the solution

= 2 e^{x} x - 5 e^{x} + C

\int \frac{30}{x ^{3} - x ^{2} - 6 x} d x

\int (3 - 5 x)^{6} d x

\int sin (2 x) \cdot e^{c o s (x)} d x

\int e^{3 + x} d x

\int x^{20} d x