What is the integral of (csc^4(θ)) ?

The integral of (csc^4(θ)) is -1/3 csc^3(θ)cos(θ)-2/3 cot(θ)+C

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integral of (csc^4(θ))

\int (csc^{4} (θ)) d θ

- \frac{1}{3} csc^{3} (θ) cos (θ) - \frac{2}{3} cot (θ) + C

Solution steps

\int csc^{4} (θ) d θ

Apply Integral Reduction

= - \frac{cos ( θ ) csc ^{3} ( θ )}{3} + \frac{2}{3} \cdot \int csc^{2} (θ) d θ

\int csc^{2} (θ) d θ = - cot (θ)

= - \frac{cos ( θ ) csc ^{3} ( θ )}{3} + \frac{2}{3} (- cot (θ))

Simplify

- \frac{cos ( θ ) csc ^{3} ( θ )}{3} + \frac{2}{3} (- cot (θ)) : - \frac{1}{3} csc^{3} (θ) cos (θ) - \frac{2}{3} cot (θ)

= - \frac{1}{3} csc^{3} (θ) cos (θ) - \frac{2}{3} cot (θ)

Add a constant to the solution

= - \frac{1}{3} csc^{3} (θ) cos (θ) - \frac{2}{3} cot (θ) + C

\frac{d}{d x} ((2 x^{3} - 4 x^{2}) (3 x^{5} + x^{2}))

\int \frac{2}{x ^{2} + 3 x - 4} d x

\int_{0}^{π} cos (\frac{x}{2}) d x

x \to 1 - lim (\frac{∣ - 1 ∣}{- 1})

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 25})

What is the integral of (csc^4(θ)) ?
The integral of (csc^4(θ)) is -1/3 csc^3(θ)cos(θ)-2/3 cot(θ)+C