1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Easy integral

  1. Jul 6, 2008 #1
    \int \frac{x \cos(x) - \sin(x)}{( x-\sin(x))^2}\ \mbox{d}x

    I don't see which substitution I should use can anyone help me?
  2. jcsd
  3. Jul 6, 2008 #2


    User Avatar
    Science Advisor
    Homework Helper

    The integrand looks a lot like something you'd get if you differentiated an expression of the form f(x)/g(x) using the quotient rule.
  4. Jul 7, 2008 #3
    That I know, but it isn't helping me. I'm interested in a structured manner of solving this problem.
  5. Jul 7, 2008 #4

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    So guessing a substitution is structured, but noting the form of the integrand is 'unstructured'? That seems like a highly arbitrary choice to make. Since integrals are generically impossible to do by hand, I'd take what you can get when you can get it.
  6. Jul 7, 2008 #5
    Indeed, with morphism's observation, a keen eye, and some algebra, you can easily arrive at the solution without any significant integration. But I have no other useful suggestion if your intent is otherwise.
  7. Jul 7, 2008 #6
    Fine. So how do I proceed next? I'm seeing something of a quotient rule but how can you find the primitive?
  8. Jul 7, 2008 #7


    User Avatar
    Science Advisor
    Homework Helper

    Just guess. Write down the form of (f(x)/g(x))'. What's a good guess for g(x)? Put that in. That's easy. Now start hunting for an f(x) that works.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook