What is the integral of (x/2+5)^{19} ?

The integral of (x/2+5)^{19} is 1/10485760 (x+10)^{20}+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (x/2+5)^{19}

\int (\frac{x}{2} + 5)^{19} d x

\frac{1}{10485760} (x + 10)^{20} + C

Solution steps

\int (\frac{x}{2} + 5)^{19} d x

Apply u-substitution

= \int u^{19} \cdot 2 d u

Take the constant out:

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

= 2 \cdot \int u^{19} d u

Apply the Power Rule

= 2 \cdot \frac{u ^{20}}{20}

Substitute back

u = \frac{x}{2} + 5

= 2 \cdot \frac{( \frac{x}{2} + 5 ) ^{20}}{20}

Simplify

2 \cdot \frac{( \frac{x}{2} + 5 ) ^{20}}{20} : \frac{1}{10485760} (x + 10)^{20}

= \frac{1}{10485760} (x + 10)^{20}

Add a constant to the solution

= \frac{1}{10485760} (x + 10)^{20} + C

What is the integral of (x/2+5)^{19} ?
The integral of (x/2+5)^{19} is 1/10485760 (x+10)^{20}+C