Results 1 to 4 of 4

Math Help - Help me to find the solution for this math problem ?

  1. #1
    Newbie
    Joined
    Aug 2009
    Posts
    16

    Help me to find the solution for this math problem ?

    Please help me to find the solution for this math problem ? \int cos^3 x + sin^5 x =
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,656
    Thanks
    1480
    Quote Originally Posted by wizard654zzz View Post
    Please help me to find the solution for this math problem ? \int cos^3 x + sin^5 x =
    Make use of the following identities:

    \cos^3{x} = \frac{3}{4}\cos{x} + \frac{1}{4}\cos{(3x)}

    and

    \sin^5{x} = \frac{5}{8}\sin{x} - \frac{5}{16}\sin{(3x)} + \frac{1}{16}\sin{(5x)}.


    So \int{\cos^3{x} + \sin^5{x}\,dx} = \int{\frac{3}{4}\cos{x} + \frac{1}{4}\cos{(3x)} + \frac{5}{8}\sin{x} - \frac{5}{16}\sin{(3x)} + \frac{1}{16}\sin{(5x)}\,dx}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by wizard654zzz View Post
    Please help me to find the solution for this math problem ? \int cos^3 x + sin^5 x =

    Put \int \cos x(1-\sin^2\!\!x)\,dx+\int \sin^3\!\!x(1-\cos^2\!\!x)\,dx= \int \cos x\,dx\,-\int \cos x\sin^2\!\!x\,dx\,+\int\sin x(1-\cos^2\!\!x)\,dx\,-\int\sin x(1-\cos^2\!\!x)\cos^2\!\!x\,dx=

    =\int \cos x\,dx\,-\int \cos x\sin^2\!\!x\,dx\,+\int\sin x\,dx\,-\int\sin x\cos^2\!\!x\,dx\,-\int\sin x\cos^2\!\!x\,dx\,+ \int\sin x\cos^4\!\!x\,dx

    Now, you have integrals of the form \int f'(x)f(x)^n\,dx=\frac{f(x)^{n+1}}{n+1} and also immediate integrals, so you're done.

    Tonio
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,656
    Thanks
    1480
    Quote Originally Posted by tonio View Post
    Put \int \cos x(1-\sin^2\!\!x)\,dx+\int \sin^3\!\!x(1-\cos^2\!\!x)\,dx= \int \cos x\,dx\,-\int \cos x\sin^2\!\!x\,dx\,+\int\sin x(1-\cos^2\!\!x)\,dx\,-\int\sin x(1-\cos^2\!\!x)\cos^2\!\!x\,dx=

    =\int \cos x\,dx\,-\int \cos x\sin^2\!\!x\,dx\,+\int\sin x\,dx\,-\int\sin x\cos^2\!\!x\,dx\,-\int\sin x\cos^2\!\!x\,dx\,+ \int\sin x\cos^4\!\!x\,dx

    Now, you have integrals of the form \int f'(x)f(x)^n\,dx=\frac{f(x)^{n+1}}{n+1} and also immediate integrals, so you're done.

    Tonio
    Mine is easier, as it doesn't involve u-substitutions.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Find the general solution to this linear operator problem:
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 30th 2010, 04:28 AM
  2. Replies: 2
    Last Post: September 7th 2009, 02:01 PM
  3. Solution to math problem
    Posted in the Algebra Forum
    Replies: 6
    Last Post: August 16th 2009, 03:59 PM
  4. Replies: 3
    Last Post: February 16th 2008, 03:58 PM
  5. Replies: 3
    Last Post: April 23rd 2007, 06:08 PM

Search Tags


/mathhelpforum @mathhelpforum