Question

Determine the integral of x^2cosec x^3 cot x^3 dx

Answer 1

Do the substitution u=x^3.
Also the integral of csc(x)cot(x) is -csc(x).

Answer 2

Proof of ∫csc(x)cot(x)=-csc(x)+C:
\[ \int{\csc(x)\cot(x)\,dx}=\int{\frac{1}{\sin(x)}\frac{\cos(x)}{\sin(x)}\,dx} \]
[Substitute u=sin(x), du=cos(x)dx]
\[ = \int{\frac{du}{u^2}} =-\frac{1}{u}+C=-\frac{1}{\sin(x)}+C=-\csc(x)+C \]

Answer 3

Ok great,thanx alot!!! :)