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

The integral of (2x-2)e^{3x} is 2(1/3 e^{3x}x-4/9 e^{3x})+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (2x-2)e^{3x}

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

2 (\frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x}) + C

Solution steps

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

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

= \int 2 (x - 1) e^{3 x} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int (x - 1) e^{3 x} d x

Apply Integration By Parts

: \frac{1}{3} e^{3 x} (x - 1) - \int \frac{1}{3} e^{3 x} d x

= 2 (\frac{1}{3} e^{3 x} (x - 1) - \int \frac{1}{3} e^{3 x} d x)

\int \frac{1}{3} e^{3 x} d x = \frac{1}{9} e^{3 x}

= 2 (\frac{1}{3} e^{3 x} (x - 1) - \frac{1}{9} e^{3 x})

Expand

\frac{1}{3} e^{3 x} (x - 1) - \frac{1}{9} e^{3 x} : \frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x}

= 2 (\frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x})

Add a constant to the solution

= 2 (\frac{1}{3} e^{3 x} x - \frac{4}{9} e^{3 x}) + C

\int \frac{8 x ^{2} + 2}{2 x ^{3} + x} d x

\int \frac{7}{5 x 25 x ^{2} - 7} d x

\int 3 cot^{3} (x) csc (x) d x

\int \frac{3 x ^{2} + 7 x - 5}{3 x + 2} d x

What is the integral of (2x-2)e^{3x} ?
The integral of (2x-2)e^{3x} is 2(1/3 e^{3x}x-4/9 e^{3x})+C