What is the integral of (2x+10)^{20} ?

The integral of (2x+10)^{20} is 1/42 (2x+10)^{21}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (2x+10)^{20}

\int (2 x + 10)^{20} d x

\frac{1}{42} (2 x + 10)^{21} + C

Solution steps

\int (2 x + 10)^{20} d x

Apply u-substitution

= \int \frac{u ^{20}}{2} d u

Take the constant out:

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

= \frac{1}{2} \cdot \int u^{20} d u

Apply the Power Rule

= \frac{1}{2} \cdot \frac{u ^{21}}{21}

Substitute back

u = 2 x + 10

= \frac{1}{2} \cdot \frac{( 2 x + 10 ) ^{21}}{21}

Simplify

\frac{1}{2} \cdot \frac{( 2 x + 10 ) ^{21}}{21} : \frac{1}{42} (2 x + 10)^{21}

= \frac{1}{42} (2 x + 10)^{21}

Add a constant to the solution

= \frac{1}{42} (2 x + 10)^{21} + C

\int sin (arctan (x)) d x

\int 48 x d x

\int \frac{x}{x ^{2} - 25} d x

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

\int \frac{x - 10}{x ^{3}} d x

What is the integral of (2x+10)^{20} ?
The integral of (2x+10)^{20} is 1/42 (2x+10)^{21}+C