Integrating cot^4 x (csc^4 x) dx Using Identities and U Substitution

[johnhuntsman]

∫(cot^4 x) (csc^4 x) dx

Wolfram wants to use the reduction formula, but I'm meant to do this just using identities and u substitution. I was thinking something along the lines of:

=∫cot^4 x (cot^2 x + 1)^2 dx

=∫cot^8 x + 2cot^6 x + cot^4 x dx

but I don't know where to go from there.

 

[stephenkeiths]

Try ∫(cot^4 x) (1+cot^2 x) (csc^2 x) dx

Whats the derivative of cot(x)?

 

[johnhuntsman]

Thanks. Worked it out with that in mind. I appreciate it : D