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

The integral of \sqrt[3]{ax} is \sqrt[3]{a} 3/4 x^{4/3}+C

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integral of \sqrt[3]{ax}

\int 3 a x d x

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

Solution steps

\int 3 a x d x

3 a x = 3 a 3 x

= \int 3 a 3 x d x

Take the constant out:

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

= 3 a \cdot \int 3 x d x

Apply the Power Rule

: \frac{3}{4} x^{\frac{4}{3}}

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

Add a constant to the solution

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

x \to 3 - lim (\frac{1}{x ^{2} - 9})

x \to 2 lim (\frac{4 - x ^{2}}{x})

y = x + x, (16, 20)

\frac{d y}{d x} + e^{x} y = 1

- x^{2} + 5 x + a

What is the integral of \sqrt[3]{ax} ?
The integral of \sqrt[3]{ax} is \sqrt[3]{a} 3/4 x^{4/3}+C