What is expand e^{2x}(1+e^{2x})^3dx ?

The solution to expand e^{2x}(1+e^{2x})^3dx is e^{2x}dx+3e^{4x}dx+3e^{6x}dx+e^{8x}dx

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

expand e^{2x}(1+e^{2x})^3dx

expand

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

e^{2 x} d x + 3 e^{4 x} d x + 3 e^{6 x} d x + e^{8 x} d x

Solution steps

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

(1 + e^{2 x})^{3} = 1 + 3 e^{2 x} + 3 e^{4 x} + e^{6 x}

= e^{2 x} (3 e^{2 x} + 3 e^{4 x} + e^{6 x} + 1) d x

Distribute parentheses

= e^{2 x} d x \cdot 1 + e^{2 x} d x \cdot 3 e^{2 x} + e^{2 x} d x \cdot 3 e^{4 x} + e^{2 x} d x e^{6 x}

= 1 \cdot e^{2 x} d x + 3 e^{2 x} e^{2 x} d x + 3 e^{2 x} e^{4 x} d x + e^{2 x} e^{6 x} d x

Simplify

1 \cdot e^{2 x} d x + 3 e^{2 x} e^{2 x} d x + 3 e^{2 x} e^{4 x} d x + e^{2 x} e^{6 x} d x : e^{2 x} d x + 3 e^{4 x} d x + 3 e^{6 x} d x + e^{8 x} d x

= e^{2 x} d x + 3 e^{4 x} d x + 3 e^{6 x} d x + e^{8 x} d x

(- 3) (4 x - 5 y = 3)

- 3 ((- 2, 1, 1) - (4, 3, 5))

\frac{( 4 + x ) ^{3}}{8}

3 (e^{3 t} + C e^{- t}) + 8 e^{- t}

1 + (3 x^{2} - 6 x)^{2}

What is expand e^{2x}(1+e^{2x})^3dx ?
The solution to expand e^{2x}(1+e^{2x})^3dx is e^{2x}dx+3e^{4x}dx+3e^{6x}dx+e^{8x}dx