Solve ∫ csc2θd2θ

$$\int \csc 2 \theta d 2 \theta$$

Evaluate

$$\frac{x}{\sin(2d_{2}\theta ^{2})}+С$$

$$d_{2}\neq 0\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\frac{\sqrt{\frac{2\pi n_{1}}{d_{2}}}}{2}\text{ and }\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =-\frac{\sqrt{\frac{2\pi n_{1}}{d_{2}}}}{2}$$

Solution Steps

Find the integral of \frac{1}{\sin(2d_{2}\theta ^{2})} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x}{\sin(2d_{2}\theta ^{2})}$$

Simplify.

$$\frac{x}{\sin(2\theta ^{2}d_{2})}$$

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.

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

Differentiate w.r.t. x

$$\frac{1}{\sin(2d_{2}\theta ^{2})}$$