What is the integral of \sqrt[3]{(csc(x))^2cot^3(x)} ?

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

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integral of \sqrt[3]{(csc(x))^2cot^3(x)}

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

Solution steps

Apply u-substitution

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

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

Apply the Power Rule

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

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

Substitute back

u = csc (x)

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

Add a constant to the solution

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

\int 2 cos (4 x) e^{s i n (4 x)} d x

2 n d

f (x) = \frac{1 + 2 x}{3 + x}, at x = 2

\frac{\partial}{\partial x} (5 2 x + 2 y)

\frac{d}{d x} y = (5 - x)^{63}

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