Question

$$\int\frac{tg\ 3x-ctg\ 3x}{\sin\ 3x}dx.$$

Answer

$$(e^2*IM*n*t^2*g*r*a*d*x*(tan(3*x)-cot(3*x)))/sin(3*x)$$

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{\imath ntegrate(\tan{3x}-\cot{3x})dx}{\sin{3x}}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{\imath n{t}^{2}{e}^{2}gra(\tan{3x}-\cot{3x})dx}{\sin{3x}}\]
Regroup terms.
\[\frac{{e}^{2}\imath n{t}^{2}gradx(\tan{3x}-\cot{3x})}{\sin{3x}}\]