anonymous 5 years ago evaluate the indefinite integral. sec(x)^21tan(x)dx

alright , we have :$\int\limits \sec^{21}(x)\tan(x) dx$ you can write it down as : $\int\limits \sec^{20}(x) \tan(x)\sec(x) dx$ now let : u = sec(x) du = tan(x)sec(x) so now you'll get: $\int\limits u^{20} du = \frac{u^{21}}{21} + c$ $= \frac{\sec^{21}(x)}{21} + c$ correct me if I'm wrong ^_^