Solve ∫ cos(n-a)/sin(n-a) wrt x

$$\int \frac { \cos ( n - a ) } { \sin ( n - a ) } d x$$

Evaluate

$$x\cot(n-a)+С$$

$$\nexists n_{1}\in \mathrm{Z}\text{ : }n=\pi n_{1}+a$$

Solution Steps

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

$$\frac{\cos(n-a)}{\sin(n-a)}x$$

Simplify.

$$\frac{\cos(n-a)x}{\sin(n-a)}$$

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.

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

Differentiate w.r.t. x

$$\cot(n-a)$$