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

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

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

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

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

Solution steps

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

Apply u-substitution

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

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

Take the constant out:

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

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

Apply the Power Rule

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

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

Substitute back

u = 1 - x

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

Add a constant to the solution

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

g (x) = 3 arccos (\frac{x}{2})

n = 1 \sum \infty \frac{4 ^{n}}{n + 1}

n = 1 \sum \infty \frac{1}{n ( n + 8 )}

168 (2 x + 5)^{5}

\frac{d}{d x} (lo g_{7} (x^{2} - 7))

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