Tuesday
September 30, 2014

Homework Help: calculus

Posted by Joshua on Saturday, May 2, 2009 at 4:14pm.

We're doing indefinite integrals using the substitution rule right now in class.
The problem:
(integral of) (e^6x)csc(e^6x)cot(e^6x)dx
I am calling 'u' my substitution variable. I feel like I've tried every possible substitution, but I still haven't found the right one.
The most promising substitution:
u= csc(e^6x)
du/dx=-(e^6x)csc(e^6x)cot(e^6x)
du/((-e^6x)csc(e^6x)cot(e^6x))=dx
so my equation would become
(integral of) usin(e^6x)
Now I don't know what to do, because we haven't learned how to the problem like this. I feel like there must be some substitution that will leave me with only one term to integrate, but I don't think I've found it. Suggestions?

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