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

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

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

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

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

Solution steps

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

Apply u-substitution

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

= \int \frac{csc ^{2} ( 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^{2} (u) d u

Use the common integral:

\int csc^{2} (u) d u = - cot (u)

= \frac{1}{3} (- cot (u))

Substitute back

u = x^{3}

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

Simplify

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

Add a constant to the solution

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

x \to \infty lim (\frac{an + 1}{an})

\int_{0}^{1} y - y^{2} d y

f (x) = tan (ln (a x + b))

\frac{\partial}{\partial x} (y + sin (x))

8 e^{3 x}

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