Results 1 to 6 of 6

Math Help - Integrating x^3 * csc^3((pi*x^2)/2)

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    19

    Integrating x^3 * csc^3((pi*x^2)/2)

    I have been having a problem trying to calculate this integral:

    \int{\frac {{x}^{3}}{ \left( \sin \left( 1/2\,\pi\,{x}^{2} \right) <br />
 \right) ^{3}}}<br />

    and the function:
    \int{\frac {{x}^{5}}{ \left( \sin \left( 1/2\,\pi\,{x}^{2} \right) <br />
 \right) ^{5}}}<br />

    If someone could give me a start on it that would be amazing!

    Thank you in advance

    MT
    Last edited by robotENGR; April 3rd 2011 at 07:17 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Junior Member BayernMunich's Avatar
    Joined
    Jul 2010
    Posts
    25
    They are unelementary integrals.
    You can not solve them using elementary methods.
    Did you post the whole question?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,311
    Thanks
    1286
    I'm not so sure they are not "elementary". They certanly can be simplified. In each case, let u= \frac{\pi x^2}{2} so that du= \pi x dx and \frac{1}{\pi}du= xdx. Also, x^2= \frac{u}{\pi}.

    Now factor an "x" out of the numerator:
    \int \frac{x^3 dx}{sin((1/2)\pi x^2)}= \int \frac{(x^2)(xdx)}{sin((1/2)\pi x^2)} = \int\fra{(u/\pi)(\frac{1}{pi}du}{sin(u)}= \frac{1}{\pi^2}\int u csc(u)du

    Similarly, \int \frac{x^5 dx}{sin((1/2)\pi x^2)}= \frac{1}{\pi^3}\int u^2 csc(u)du

    Try integration by parts now.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Nov 2009
    Posts
    19
    I did post the correct integral I need to solve.

    HallsofIvy:

    I think my whole issue is keeps coming down to solving:

    \int{u*csc{(u)} du}

    I tried to use integration by parts but in the last integrand I get a nasty equation for which I don't have the experience to integrate.

    Thanks for your incite!
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,311
    Thanks
    1286
    Yeah, I just looked up the anti-derivative of cosecant- and it isn't easy! So perhaps BayernMunich was right to begin with!
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Nov 2009
    Posts
    19
    I think I will just approximate the integral using a series expansion

    Thanks for your help!

    MT
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. need help on integrating this
    Posted in the Calculus Forum
    Replies: 3
    Last Post: June 4th 2010, 06:29 AM
  2. Integrating
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 2nd 2010, 11:57 AM
  3. integrating
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 31st 2010, 02:18 PM
  4. integrating e
    Posted in the Calculus Forum
    Replies: 3
    Last Post: April 27th 2010, 11:03 PM
  5. Integrating (2x^2 -3)/x(x^2 +4
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 17th 2010, 06:14 AM

Search Tags


/mathhelpforum @mathhelpforum