What is the integral of e^x(5-2e^x)^2 ?

The integral of e^x(5-2e^x)^2 is 25e^x-10e^{2x}+4/3 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 e^x(5-2e^x)^2

\int e^{x} (5 - 2 e^{x})^{2} d x

25 e^{x} - 10 e^{2 x} + \frac{4}{3} e^{3 x} + C

Solution steps

\int e^{x} (5 - 2 e^{x})^{2} d x

5 - 2 e^{x} = 5 (1 - \frac{2 e ^{x}}{5})

= \int e^{x} (5 (1 - \frac{2 e ^{x}}{5}))^{2} d x

Simplify

e^{x} (5 (1 - \frac{2 e ^{x}}{5}))^{2} : 25 e^{x} - 20 e^{2 x} + 4 e^{3 x}

= \int 25 e^{x} - 20 e^{2 x} + 4 e^{3 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 25 e^{x} d x - \int 20 e^{2 x} d x + \int 4 e^{3 x} d x

\int 25 e^{x} d x = 25 e^{x}

\int 20 e^{2 x} d x = 10 e^{2 x}

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

= 25 e^{x} - 10 e^{2 x} + \frac{4}{3} e^{3 x}

Add a constant to the solution

= 25 e^{x} - 10 e^{2 x} + \frac{4}{3} e^{3 x} + C

\int \frac{( x ^{2} - 3 x + 8 )}{( x ^{2} - 4 x + 7 ) ^{2}} d x

\int 200 + 200 cos (x) d x

\int \frac{1}{h - 19} d h

\int \frac{x}{x ^{2} - 20 x + 84} d x

\int \frac{1}{x ( 9 ln ( x ) + 8 )} d x

What is the integral of e^x(5-2e^x)^2 ?
The integral of e^x(5-2e^x)^2 is 25e^x-10e^{2x}+4/3 e^{3x}+C