Solve ∫ csc^4t

$$\int \csc ^ { 4 } t$$

Evaluate

$$\frac{x}{\left(\sin(t)\right)^{4}}+С$$

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

Solution Steps

Find the integral of \frac{1}{\left(\sin(t)\right)^{4}} using the table of common integrals rule \int a\mathrm{d}x=ax.

$$\frac{x}{\left(\sin(t)\right)^{4}}$$

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.

$$\begin{matrix}\frac{x}{\left(\sin(t)\right)^{4}}+С_{3},&\end{matrix}$$

Differentiate w.r.t. x

$$\frac{1}{\left(\sin(t)\right)^{4}}$$