How do you Integrate?
int sec^6x
1 Answer
May 4, 2018
Explanation:
We want to integrate
I=intsec^6(x)dx
Rewrite the integrand using the trig identity
color(blue)(sec^2(x)=1+tan^2(x)
I=intsec^2(x)(sec^2(x))^2dx
color(white)(I)=intsec^2(x)(1+tan^2(x))^2dx
Make a substitution
I=int(1+u^2)^2du
color(white)(I)=intu^4+2u^2+1du
color(white)(I)=1/5u^5+2/3u^3+u+C
Substitute back
I=1/5tan^5(x)+2/3tan^3(x)+tan(x)+C