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

The integral of x^{(-2)/3}sqrt(x^{1/3)-2} is 2(\sqrt[3]{x}-2)^{3/2}+C

Popular >

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

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

Solution steps

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

Apply u-substitution

: \int 3 u d u

= \int 3 u d u

Take the constant out:

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

= 3 \cdot \int u d u

Apply the Power Rule

: \frac{2}{3} u^{\frac{3}{2}}

= 3 \cdot \frac{2}{3} u^{\frac{3}{2}}

Substitute back

u = x^{\frac{1}{3}} - 2

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

Simplify

Add a constant to the solution

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

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

\frac{d}{d x} (\frac{x ^{3}}{4} + \frac{1}{3 x})

\int 2 d x

x \to 1 lim ([5 f (x) + g (x)])

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