How do you find the integral of #tan^3(2x) sec^100(2x) dx#?
1 Answer
Mar 23, 2018
Explanation:
We want to solve
#I=inttan^3(2x)sec^100(2x)dx#
Make a substitution
#I=1/2inttan^3(u)sec^100(u)du#
Use the identity
#I=1/2inttan(u)(sec^2(u)-1)sec^100(u)du#
Make a substitution
#I=1/2int(s^2-1)s^99du#
#color(white)(I)=1/2ints^101-s^99du#
#color(white)(I)=1/204s^102-1/200s^100#
Substitute back
#I=1/204sec^102(2x)-1/200sec^100(2x)+C#