What is the integral of \sqrt[5]{ax^3} ?

The integral of \sqrt[5]{ax^3} is (5\sqrt[5]{a}x^{8/5})/8+C

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integral of \sqrt[5]{ax^3}

Solution steps

Apply u-substitution

Take the constant out:

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

Apply the Power Rule

: \frac{15}{8} u^{\frac{8}{15}}

Substitute back

u = x^{3}

Simplify

Add a constant to the solution

f (x) = ln (x + x^{2} + 1)

\int 49 - t^{2} d t

\frac{\partial}{\partial x} (e^{- 4 x} cos (5 x))

\frac{\partial}{\partial x} (\frac{( x - 3 y )}{x + 3 y})

\frac{d}{d x} (t e^{2 x})

What is the integral of \sqrt[5]{ax^3} ?
The integral of \sqrt[5]{ax^3} is (5\sqrt[5]{a}x^{8/5})/8+C