Chapter 7 - Integration Techniques - 7.3 Trigonometric Integrals - 7.3 Exercises - Page 529: 7

$${\text{Let }}u = \tan x$$

$$\eqalign{ & \int {{{\tan }^{10}}x{{\sec }^2}xdx} \cr & {\text{The method to solve tis integral is :}} \cr & {\text{Set }}u = \tan x,\,\,\,then\,\,\,\,\,du = {\sec ^2}xdx \cr & \cr & {\text{Apply the substitution}} \cr & \int {{{\tan }^{10}}x{{\sec }^2}xdx} = \int {{u^{10}}du} \cr & {\text{Then, using the power rule for integration we can solve}} \cr & {\text{easily}}{\text{.}} \cr} $$