Chapter 7 - Principles Of Integral Evaluation - 7.3 Integrating Trigonometric Functions - Exercises Set 7.3 - Page 507: 54

$${\text{False }}$$

$$\eqalign{ & \int {{{\sin }^8}x{{\cos }^5}x} dx \cr & {\text{Rewrite the integrand}} \cr & = \int {{{\sin }^8}x{{\cos }^4}x\cos x} dx \cr & = \int {{{\sin }^8}x{{\left( {{{\cos }^2}x} \right)}^2}\cos x} dx \cr & {\text{Use the trigonometric identity }}{\cos ^2}x = 1 - {\sin ^2}x \cr & = \int {{{\sin }^8}x{{\left( {1 - {{\sin }^2}x} \right)}^2}\cos x} dx \cr & {\text{Now, set }}u = \sin x. \cr & {\text{Therefore, the statement is false}}{\text{.}} \cr} $$