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

The integral of (1+2e^{3x})^3e^{3x} is 1/3 e^{3x}+e^{6x}+4/3 e^{9x}+2/3 e^{12x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (1+2e^{3x})^3e^{3x}

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

\frac{1}{3} e^{3 x} + e^{6 x} + \frac{4}{3} e^{9 x} + \frac{2}{3} e^{12 x} + C

Solution steps

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

Expand

(1 + 2 e^{3 x})^{3} e^{3 x} : e^{3 x} + 6 e^{6 x} + 12 e^{9 x} + 8 e^{12 x}

= \int e^{3 x} + 6 e^{6 x} + 12 e^{9 x} + 8 e^{12 x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int e^{3 x} d x + \int 6 e^{6 x} d x + \int 12 e^{9 x} d x + \int 8 e^{12 x} d x

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

\int 6 e^{6 x} d x = e^{6 x}

\int 12 e^{9 x} d x = \frac{4}{3} e^{9 x}

\int 8 e^{12 x} d x = \frac{2}{3} e^{12 x}

= \frac{1}{3} e^{3 x} + e^{6 x} + \frac{4}{3} e^{9 x} + \frac{2}{3} e^{12 x}

Add a constant to the solution

= \frac{1}{3} e^{3 x} + e^{6 x} + \frac{4}{3} e^{9 x} + \frac{2}{3} e^{12 x} + C

\int (x^{3} + 5 x^{2}) sin (3 x) d x

\int 5 x e^{- 15 x} d x

\int \frac{sinh ( x )}{( 1 + cosh ( x ) ) ^{3}} d x

\int x (3 x + 2)^{\frac{3}{2}} d x

\int \frac{1}{9 x + x ln ^{2} ( x )} d x

What is the integral of (1+2e^{3x})^3e^{3x} ?
The integral of (1+2e^{3x})^3e^{3x} is 1/3 e^{3x}+e^{6x}+4/3 e^{9x}+2/3 e^{12x}+C