Chapter 8: Techniques of Integration - Section 8.1 - Using Basic Integration Formulas - Exercises 8.1 - Page 448: 4

$$\int_{\pi/4}^{\pi/3}\frac{dx}{cos^{2}x\,tan\,x}=\frac{ln3}{2}$$

$$\int_{\pi/4}^{\pi/3}\frac{dx}{cos^{2}x\,tan\,x}=\int_{\pi/4}^{\pi/3}\frac{sec^{2}x}{tan\,x}dx$$ $$=\int_{\pi/4}^{\pi/3}\frac{d(tan\,x)}{tan\,x}$$ $$=\left | ln(tan\,x) \right |_{\pi/4}^{\pi/3}$$ $$=ln\sqrt{3}-ln1$$ $$=\frac{ln3}{2}$$