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Popular Calculus >

integral of (ax)^3

Solution

\int (a x)^{3} d x

Solution

\frac{a ^{3} x ^{4}}{4} + C

Solution steps

\int (a x)^{3} d x

Apply exponent rule:

(a \cdot b)^{n} = a^{n} b^{n}

= \int a^{3} x^{3} d x

Take the constant out:

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

= a^{3} \cdot \int x^{3} d x

Apply the Power Rule

= a^{3} \frac{x ^{4}}{4}

Multiply fractions:

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

= \frac{a ^{3} x ^{4}}{4}

Add a constant to the solution

= \frac{a ^{3} x ^{4}}{4} + C

Graph

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Frequently Asked Questions (FAQ)

What is the integral of (ax)^3 ?
The integral of (ax)^3 is (a^3x^4)/4+C