What is the integral of (ax)^n ?

The integral of (ax)^n is (a^nx^{n+1})/(n+1)+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of (ax)^n

\int (a x)^{n} d x

\frac{a ^{n} x ^{n + 1}}{n + 1} + C

Solution steps

\int (a x)^{n} d x

(a x)^{n} = a^{n} x^{n}

= \int a^{n} x^{n} d x

Take the constant out:

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

= a^{n} \cdot \int x^{n} d x

Apply the Power Rule

= a^{n} \frac{x ^{n + 1}}{n + 1}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{a ^{n} x ^{n + 1}}{n + 1}

Add a constant to the solution

= \frac{a ^{n} x ^{n + 1}}{n + 1} + C