Integrate csc^3 2x dx ?
2 Answers
Explanation:
We want to solve
I=∫csc3(2x)dx
Make a substitution
I=12∫csc3(u)du
Use tangent half-angle substitution
then
I=12∫(1+s22s)321+s2ds
I=∫(1+s2)28s3ds
I=18∫s4+2s2+1s3ds
I=18∫s+2s−1+s−3ds
I=18(12s2+2ln(s)−12s−2)+C
I=116(s2+4ln(s)−1s2)+C
Substitute back
I=116(tan2(x)+4ln(tan(x))−1tan2(x))+C
Explanation:
Here,
Let,
We know that,
substituting back