What is the integral of 1/((5x-2)^{2/3)} ?

The integral of 1/((5x-2)^{2/3)} is 3/5 (5x-2)^{1/3}+C

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integral of 1/((5x-2)^{2/3)}

\int \frac{1}{( 5 x - 2 ) ^{\frac{2}{3}}} d x

\frac{3}{5} (5 x - 2)^{\frac{1}{3}} + C

Solution steps

\int \frac{1}{( 5 x - 2 ) ^{\frac{2}{3}}} d x

Apply u-substitution

: \int \frac{1}{5 u ^{\frac{2}{3}}} d u

= \int \frac{1}{5 u ^{\frac{2}{3}}} d u

Take the constant out:

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

= \frac{1}{5} \cdot \int \frac{1}{u ^{\frac{2}{3}}} d u

Apply the Power Rule

: 3 u^{\frac{1}{3}}

= \frac{1}{5} \cdot 3 u^{\frac{1}{3}}

Substitute back

u = 5 x - 2

= \frac{1}{5} \cdot 3 (5 x - 2)^{\frac{1}{3}}

Simplify

\frac{1}{5} \cdot 3 (5 x - 2)^{\frac{1}{3}} : \frac{3}{5} (5 x - 2)^{\frac{1}{3}}

= \frac{3}{5} (5 x - 2)^{\frac{1}{3}}

Add a constant to the solution

= \frac{3}{5} (5 x - 2)^{\frac{1}{3}} + C

\frac{d}{d x} (x^{4} - 2 x^{2} - 3)

\int \frac{x + 7}{x ^{2} + 25} d x

\int x cos (3 x^{2}) d x

x \to 0 lim (\frac{1 + x}{x})

y = (5 x^{2} + x) (x - x^{2})

What is the integral of 1/((5x-2)^{2/3)} ?
The integral of 1/((5x-2)^{2/3)} is 3/5 (5x-2)^{1/3}+C