Solve ∫ csc^3edθ

$$\int \csc ^ { 3 } e d \theta$$

Evaluate

$$\frac{\theta }{\left(\sin(e)\right)^{3}}+С$$

Solution Steps

Find the integral of \frac{1}{\left(\sin(e)\right)^{3}} using the table of common integrals rule \int a\mathrm{d}\theta =a\theta .

$$\frac{\theta }{\left(\sin(e)\right)^{3}}$$

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

$$\frac{\theta }{\left(\sin(e)\right)^{3}}+С$$

Differentiate w.r.t. θ

$$\frac{1}{\left(\sin(e)\right)^{3}}$$