Results 1 to 6 of 6

Math Help - Integral of 1/1+sinx

  1. #1
    Newbie
    Joined
    Nov 2008
    Posts
    14

    Integral of 1/1+sinx

    How do you integrate this:
    \int \frac {1}{1+sinx}dx

    I tried expanding the '1' as sin^2 x+cos^2 x
    And then i tried multiplying numerator and denominator by cos x.. But it was of no use..

    What do you do generally, when you have a trigonometric equation in the denominator??
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,617
    Thanks
    1581
    Awards
    1

    Re: Integral of 1/1+sinx

    Quote Originally Posted by animesh271094 View Post
    How do you integrate this:
    \int \frac {1}{1+sinx}dx
    It is true that \frac {1}{1+sinx}=\frac{1-\sin(x)}{\cos^2(x)}=\sec^2(x)+\frac{-\sin(x)}{\cos^2(x)}
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2008
    Posts
    14

    Re: Integral of 1/1+sinx

    Alright.. thanx..
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Integral of 1/1+sinx

    Another way is with the Weierstrass substitution:
    Let t=\tan \left(\frac{x}{2}\right) and so the integral becomes:
    \int \frac{\frac{2}{1+t^2}}{1+\frac{2t}{1+t^2}}dt
    =\int \left(\frac{2}{1+t^2}\cdot \frac{1+t^2}{1+t^2+2t}\right)dt
    =\int \frac{2dt}{t^2+2t+1}dt=\int \frac{2dt}{(t+1)\cdot (t+1)}

    Now split in partial fractions.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13

    Re: Integral of 1/1+sinx

    Why partial fractions when having t^2+2t+1=(t+1)^2 ?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Integral of 1/1+sinx

    Yes, offcourse! I was to busy with partial fractions I didn't noticed that, thanks .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] integral abs sinx [0,3pi/2]
    Posted in the Calculus Forum
    Replies: 9
    Last Post: August 1st 2010, 10:08 PM
  2. integral of e^2x * sinx
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 31st 2010, 05:39 PM
  3. Integral of Ln(Sinx)/Sinx
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 11th 2010, 02:18 AM
  4. Integral of cos^2(x)/sinx
    Posted in the Calculus Forum
    Replies: 2
    Last Post: January 10th 2010, 11:06 AM
  5. Replies: 0
    Last Post: September 10th 2008, 07:53 PM

Search Tags


/mathhelpforum @mathhelpforum