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Popular >

integral of ax^3

Solution

\int a x^{3} d x

Solution

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

Solution steps

\int a x^{3} d x

Take the constant out:

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

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

Apply the Power Rule

: \frac{x ^{4}}{4}

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

Multiply fractions:

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

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

Add a constant to the solution

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

Popular Examples

integral of (6x^2+4x-30)/(x^3+5x^2+6x)

\int \frac{6 x ^{2} + 4 x - 30}{x ^{3} + 5 x ^{2} + 6 x} d x

integral from 3 to 4 of 1/(x^2-4)

\int_{3}^{4} \frac{1}{x ^{2} - 4} d x

derivative of f(x)=5x^2-3x+7 derivative of

f (x) = 5 x^{2} - 3 x + 7

integral of 1/(4+2sin(x))

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

derivative of e^{-5x^2}derivative of

e^{- 5 x^{2}}

Frequently Asked Questions (FAQ)

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