hi, I was wondering if someone could show me how to do a problem. I'm studying for a test...and I wanted to be prepared in case something like this came up.
how to you integrate the following...
cosine cubed of x * sin to the fifth of x dx
This happens to be a long integral.
But the first set is to use integration by part,
u=x and v'=sin^5 x
Thus, u'=1
But when you find v you need to find the integral of sin^5 x which you can do by writing it as:
sin^5 x=sin^4 x sin x = (1-cos^2x)^2*sin x
Then use the substitution t=sin x.
But after you do that long integration by parts you will need to do another trigonometric integral like the one above.