Results 1 to 3 of 3

Thread: Four trigonometric integrals.

  1. #1
    Junior Member
    Joined
    Oct 2008
    Posts
    41

    Four trigonometric integrals.

    Hello! I'm having some troubles solving this integrals so your help would be much appreciated.

    1. $\displaystyle \int \frac{dx}{tan^8x}$

    2. $\displaystyle \int \frac{dx}{\sqrt[4]{sin^3xcos^5x}}$

    3. $\displaystyle \int \frac{dx}{(sinx+cosx)^2}$

    4. $\displaystyle \frac{\sqrt{tgx}dx}{sinxcosx}$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    1)$\displaystyle I_n=\int\frac{dx}{\tan^nx}=\int\cot^nxdx=\int\cot^ {n-2}x\cdot\cot^2xdx=\int\cot^{n-2}x\left(\frac{1}{\sin^2x}-1\right)dx=$

    $\displaystyle =-\int\cot^{n-2}x\cdot(\cot x)'dx-I_{n-2}=-\frac{\cot^{n-1}x}{n-1}-I_{n-2}$

    3) $\displaystyle \sin x+\cos x=\sin x+\sin\left(\frac{\pi}{2}-x\right)=2\sin\frac{\pi}{4}\cos\left(x-\frac{\pi}{4}\right)=\sqrt{2}\cos\left(x-\frac{\pi}{4}\right)$

    Then, $\displaystyle \int\frac{dx}{2\cos^2\left(x-\frac{\pi}{4}\right)}=\frac{1}{2}\tan\left(x-\frac{\pi}{4}\right)+C$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    4. use the substitution


    $\displaystyle u = \sqrt {\tan x} $
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 4
    Last Post: Apr 30th 2010, 03:46 AM
  2. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 3
    Last Post: Nov 14th 2009, 06:52 PM
  3. trigonometric integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Mar 10th 2009, 07:45 AM
  4. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 1
    Last Post: Feb 22nd 2009, 03:14 AM
  5. Trigonometric Integrals
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 23rd 2008, 03:08 PM

Search Tags


/mathhelpforum @mathhelpforum