What is the integral of 2(1+2x)^4 ?

The integral of 2(1+2x)^4 is 1/5 (1+2x)^5+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 2(1+2x)^4

\int 2 (1 + 2 x)^{4} d x

\frac{1}{5} (1 + 2 x)^{5} + C

Solution steps

\int 2 (1 + 2 x)^{4} d x

Take the constant out:

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

= 2 \cdot \int (1 + 2 x)^{4} d x

Apply u-substitution

: \int \frac{u ^{4}}{2} d u

= 2 \cdot \int \frac{u ^{4}}{2} d u

Take the constant out:

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

= 2 \cdot \frac{1}{2} \cdot \int u^{4} d u

Apply the Power Rule

: \frac{u ^{5}}{5}

= 2 \cdot \frac{1}{2} \cdot \frac{u ^{5}}{5}

Substitute back

u = 1 + 2 x

= 2 \cdot \frac{1}{2} \cdot \frac{( 1 + 2 x ) ^{5}}{5}

Simplify

2 \cdot \frac{1}{2} \cdot \frac{( 1 + 2 x ) ^{5}}{5} : \frac{1}{5} (1 + 2 x)^{5}

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

Add a constant to the solution

= \frac{1}{5} (1 + 2 x)^{5} + C

\int (\frac{6}{x ^{4}}) d x

\frac{d}{d x} (e^{2 x} 2)

\frac{\partial}{\partial x} (x y cos (yz))

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