Solve ∫ tan(θ)

$$\int \tan ( \theta )$$

Evaluate

$$x\tan(\theta )+С$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }\theta =\pi n_{1}+\frac{\pi }{2}$$

Solution Steps

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

$$\frac{\sin(\theta )}{\cos(\theta )}x$$

Simplify.

$$\frac{\sin(\theta )x}{\cos(\theta )}$$

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.

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

Differentiate w.r.t. x

$$\tan(\theta )$$