What is the integral of (e^{3x}+6)^3e^{2x} ?

The integral of (e^{3x}+6)^3e^{2x} is 1/11 e^{11x}+9/4 e^{8x}+108/5 e^{5x}+108e^{2x}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (e^{3x}+6)^3e^{2x}

\int (e^{3 x} + 6)^{3} e^{2 x} d x

\frac{1}{11} e^{11 x} + \frac{9}{4} e^{8 x} + \frac{108}{5} e^{5 x} + 108 e^{2 x} + C

Solution steps

\int (e^{3 x} + 6)^{3} e^{2 x} d x

Expand

(e^{3 x} + 6)^{3} e^{2 x} : e^{11 x} + 18 e^{8 x} + 108 e^{5 x} + 216 e^{2 x}

= \int e^{11 x} + 18 e^{8 x} + 108 e^{5 x} + 216 e^{2 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^{11 x} d x + \int 18 e^{8 x} d x + \int 108 e^{5 x} d x + \int 216 e^{2 x} d x

\int e^{11 x} d x = \frac{1}{11} e^{11 x}

\int 18 e^{8 x} d x = \frac{9}{4} e^{8 x}

\int 108 e^{5 x} d x = \frac{108}{5} e^{5 x}

\int 216 e^{2 x} d x = 108 e^{2 x}

= \frac{1}{11} e^{11 x} + \frac{9}{4} e^{8 x} + \frac{108}{5} e^{5 x} + 108 e^{2 x}

Add a constant to the solution

= \frac{1}{11} e^{11 x} + \frac{9}{4} e^{8 x} + \frac{108}{5} e^{5 x} + 108 e^{2 x} + C

\int \frac{( x + 1 )}{4 4} (x - 1) d x

\int \frac{11 x ^{2}}{( 100 + x ^{2} ) ^{2}} d x

\int cos (\frac{x}{a}) d x

\int \frac{x cos ^{2} ( x ^{2} )}{sin ( x ^{2} )} d x

\int x^{2} cos (x n) d x

What is the integral of (e^{3x}+6)^3e^{2x} ?
The integral of (e^{3x}+6)^3e^{2x} is 1/11 e^{11x}+9/4 e^{8x}+108/5 e^{5x}+108e^{2x}+C