Expert: Paul Klarreich - 10/12/2005

Question
Hi Paul,
Your was exactly what I wanted last time.Thanks.Now, I have a question on integrals that I'm hoping you can help me with.
What's the antiderivative of {[cos(3/x)]/x^2}dx

Answer
Hi, Jeff,
Thank you for the kind comments.  After that one, this should be a cinch.

You have a function,  3/x,  whose derivative, except for a constant factor, appears as a factor of the integrand.
[VIEW IN A FIXED FONT]
So, u = 3/x,  du = - 3/x^2 dx, dx = -x^2 du/3
And the integrand becomes:
(  cos u   -x^2 du
| -------- -------
)    x^2      3

Now the x^2's cancel, -1/3 can be factored out, and you have just cos u du as the integrand.  You can take it from there.