What is the integral of e^{2x}(1-6e^{2x})^2 ?

The integral of e^{2x}(1-6e^{2x})^2 is -1/36 (1-6e^{2x})^3+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of e^{2x}(1-6e^{2x})^2

\int e^{2 x} (1 - 6 e^{2 x})^{2} d x

- \frac{1}{36} (1 - 6 e^{2 x})^{3} + C

Solution steps

\int e^{2 x} (1 - 6 e^{2 x})^{2} d x

Apply u-substitution

= \int - \frac{u ^{2}}{12} d u

Take the constant out:

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

= - \frac{1}{12} \cdot \int u^{2} d u

Apply the Power Rule

= - \frac{1}{12} \cdot \frac{u ^{3}}{3}

Substitute back

u = 1 - 6 e^{2 x}

= - \frac{1}{12} \cdot \frac{( 1 - 6 e ^{2 x} ) ^{3}}{3}

Simplify

- \frac{1}{12} \cdot \frac{( 1 - 6 e ^{2 x} ) ^{3}}{3} : - \frac{1}{36} (1 - 6 e^{2 x})^{3}

= - \frac{1}{36} (1 - 6 e^{2 x})^{3}

Add a constant to the solution

= - \frac{1}{36} (1 - 6 e^{2 x})^{3} + C

What is the integral of e^{2x}(1-6e^{2x})^2 ?
The integral of e^{2x}(1-6e^{2x})^2 is -1/36 (1-6e^{2x})^3+C