can anyone help me to integrate ∫csc^3 (x)?

Question

can anyone show me the steps how to integrate ∫csc^3 (x) please

Answer 1

That's a messy problem. Doing it by repeated parts I got (after a few trig substitutions and about 5 or 6 sheets of paper ☺)

(-1/8)(csc(x/2))^2 + (1/8)(sec(c))^2 -(1/2)ln(cos(x/2)) +
(1/2)ln(sin(x/2) + C

HTH
Doug

Answer 2

= C +0.5(ln(tan(x/2)) -cosx*(csc x)^2);