How do you find the indefinite integral of ∫ dx / sin^3 x cos^5 x ?
1 Answer
Apr 15, 2018
Explanation:
We want to solve
I=int1/(sin^3(x)cos^5(x))dx
Multiply the DEN and NUM by
an integral consisting of tangens and secant have good opputunities substitution
I=intsec^8(x)/(tan^3(x))dx
Make a substitution
I=intsec^6(x)/(u^3)du
Use the identity
I=int(u^2+1)^3/(u^3)du
color(white)(I)=int(u^6+3u^4+3u^2+1)/(u^3)du
color(white)(I)=intu^3+3u+3/u+1/u^3du
color(white)(I)=1/4u^4+3/2u^2+3ln(u)-1/(2u^2)+C
Substitute back