Solve ∫ cscθcotθ

$$\int \csc \theta \cot \theta$$

Evaluate

$$\frac{x\cot(\theta )}{\sin(\theta )}+С$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}$$

Solution Steps

Find the integral of \frac{\cos(\theta )}{\left(\sin(\theta )\right)^{2}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{\cos(\theta )}{\left(\sin(\theta )\right)^{2}}x$$

Simplify.

$$\frac{\cos(\theta )x}{\left(\sin(\theta )\right)^{2}}$$

If F\left(x\right) is an antiderivative of f\left(x\right), then the set of all antiderivatives of f\left(x\right) is given by F\left(x\right)+C. Therefore, add the constant of integration C\in \mathrm{R} to the result.

$$\begin{matrix}\frac{\cos(\theta )x}{\left(\sin(\theta )\right)^{2}}+С_{3},&\end{matrix}$$

Differentiate w.r.t. x

$$\frac{\cot(\theta )}{\sin(\theta )}$$