What is the integral of 3/5 x^{1/3} ?

The integral of 3/5 x^{1/3} is 9/20 x^{4/3}+C

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integral of 3/5 x^{1/3}

\int \frac{3}{5} x^{\frac{1}{3}} d x

\frac{9}{20} x^{\frac{4}{3}} + C

Solution steps

\int \frac{3}{5} x^{\frac{1}{3}} d x

Take the constant out:

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

= \frac{3}{5} \cdot \int x^{\frac{1}{3}} d x

Apply the Power Rule

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

= \frac{3}{5} \cdot \frac{3}{4} x^{\frac{4}{3}}

Simplify

\frac{3}{5} \cdot \frac{3}{4} x^{\frac{4}{3}} : \frac{9}{20} x^{\frac{4}{3}}

= \frac{9}{20} x^{\frac{4}{3}}

Add a constant to the solution

= \frac{9}{20} x^{\frac{4}{3}} + C

\frac{d}{d x} ((a x + b) e^{x})

f (x) = x^{2} - x + 10, at x = 3

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f (x) = 2 x^{3}, (- 2, - 16)

\int cot (3 x) d x

What is the integral of 3/5 x^{1/3} ?
The integral of 3/5 x^{1/3} is 9/20 x^{4/3}+C