What is the integral of f(3\sqrt[3]{x}) ?

The integral of f(3\sqrt[3]{x}) is 9/4 fx^{4/3}+C

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integral of f(3\sqrt[3]{x})

\int f (3 3 x) d x

\frac{9}{4} f x^{\frac{4}{3}} + C

Solution steps

\int f \cdot 3 3 x d x

Take the constant out:

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

= 3 f \cdot \int 3 x d x

Apply the Power Rule

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

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

Simplify

3 f \frac{3}{4} x^{\frac{4}{3}} : \frac{9}{4} f x^{\frac{4}{3}}

= \frac{9}{4} f x^{\frac{4}{3}}

Add a constant to the solution

= \frac{9}{4} f x^{\frac{4}{3}} + C

\frac{d}{d x} (4 x^{4} - 3 x^{3} - 30)

\int (1 - cos (2 x)) d x

\int \frac{x}{( x ^{2} + 6 x + 13 )} d x

x \to 2 lim (e^{2})

y^{^{'''}} - y^{^{''}} - 20 y^{^{'}} = 0

What is the integral of f(3\sqrt[3]{x}) ?
The integral of f(3\sqrt[3]{x}) is 9/4 fx^{4/3}+C