What is the integral of x^2csc(x^3)cot(x^3) ?

The integral of x^2csc(x^3)cot(x^3) is -1/3 csc(x^3)+C

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integral of x^2csc(x^3)cot(x^3)

\int x^{2} csc (x^{3}) cot (x^{3}) d x

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

Solution steps

\int x^{2} csc (x^{3}) cot (x^{3}) d x

Apply u-substitution

: \int \frac{u csc ( u ^{\frac{3}{2}} ) cot ( u ^{\frac{3}{2}} )}{2 x} d u

= \int \frac{csc ( u ) cot ( u )}{3} d u

Take the constant out:

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

= \frac{1}{3} \cdot \int csc (u) cot (u) d u

Apply u-substitution

: \int - 1 d v

= \frac{1}{3} \cdot \int - 1 d v

Integral of a constant:

\int a d x = a x

= \frac{1}{3} (- 1) v

Substitute back

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

Simplify

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

Add a constant to the solution

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

f (x) = - 4 x^{2} - 3 x

\frac{\partial}{\partial x} (x^{2} + y^{2} + 1)

f (x) = \frac{x}{( x - 7 ) ^{2}}

\frac{( e ^{x} + e ^{- x} )}{2}

x \to 0 lim (\frac{x}{x + ∣ x ∣})

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