Results 1 to 8 of 8

Math Help - Integrate sec x

  1. #1
    Member roshanhero's Avatar
    Joined
    Aug 2008
    Posts
    180

    Integrate sec x

    How can we integrate sec x? Please give me only hint.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by roshanhero View Post
    How can we integrate sec x? Please give me only hint.
    Let x=2\arctan(z). That is the most fundamental and fool-proof way. There are cleverer ones.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    another way is to multiply and divide sec(x) by (secx +tan(x) to obtain

    [sec^2(x) +sec(x)tan(x)]/[sec(x)+tan(x)]

    Then let u = sec(x) +tan(x)

    du = [ sec^2(x) +sec(x)tan(x)]dx

    you end up with integral[du/u] = ln(u)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Math Engineering Student
    Krizalid's Avatar
    Joined
    Mar 2007
    From
    Santiago, Chile
    Posts
    3,654
    Thanks
    13
    Multiply top and bottom by \sec x+\tan x. (Got beaten.)
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374
    multiply top and bottom by \cos x.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Calculus26's Avatar
    Joined
    Mar 2009
    From
    Florida
    Posts
    1,271
    Don't really see what multiplying top and bottom by cos(x) does for you??
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Senior Member Shanks's Avatar
    Joined
    Nov 2009
    From
    BeiJing
    Posts
    374
    Quote Originally Posted by Calculus26 View Post
    Don't really see what multiplying top and bottom by cos(x) does for you??
    After that, substitute \cos ^2x with 1-\sin ^2x, then seperate the fraction into two parts, I think you can take it from here now.
    Follow Math Help Forum on Facebook and Google+

  8. #8
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Calculus26 View Post
    Don't really see what multiplying top and bottom by cos(x) does for you??
    \int\frac{dx}{\cos(x)}=\int\frac{\cos(x)}{\cos^2(x  )}dx=\int\frac{\cos(x)}{1-\sin^2(x)}dx

    Let \sin(x)=z\implies dz=\cos(x)\text{ }dx

    So our integral becomes \int\frac{dz}{1-z^2}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integrate 3 e^x
    Posted in the Calculus Forum
    Replies: 4
    Last Post: June 9th 2010, 01:16 PM
  2. how to integrate this ??
    Posted in the Calculus Forum
    Replies: 8
    Last Post: August 9th 2009, 08:14 PM
  3. Integrate
    Posted in the Calculus Forum
    Replies: 7
    Last Post: April 28th 2009, 07:54 PM
  4. How to integrate x^x?
    Posted in the Calculus Forum
    Replies: 5
    Last Post: April 25th 2009, 07:51 PM
  5. Integrate
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 15th 2009, 03:50 PM

Search Tags


/mathhelpforum @mathhelpforum