analytic geom and calc 1

Sorry to be such a pain. the problem is that i have a korean college professor and he is very hard to understand nor does he go by the book. thats fine but when i get home to study i forget the lesson and go back to refer to my book its in another form thats hard to understand. I seem to be having some trouble with integrals; definite and indefinite; normal and using the substitution rule, for instance trying to use the substitution rule on an integral equation with cos x*sin^6 x dx and i dont know what to substitute. i'm leaning towards the sin ^6. please help or send info for help thanks!!!!!

Remember, when using the substitution rule you are reversing things of the form f(g(x))g'(x). So let u = sin x, then du = cos x. Now, you have to integrate u^6 du, which is 1/7 u^7 du or 1/7 (sin x)^7 . Now do you see what I meant by f(g(x))g'(x), we are basically undoing a derivative obtained using the chain rule.