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Math Help - Some Complex Integrals

  1. #1
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    Question Some Complex Integrals

    Hi guys , i want you to help me to figure out some Complex integral forms , that need to be memorized thank you :

    Int 1/(sec x)
    int 1/(1+x^2)
    int tan x
    int cot x
    int 1/2x

    and a quick note on int of exponential functions ,


    thanks
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  2. #2
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    Quote Originally Posted by phareouh View Post
    Hi guys , i want you to help me to figure out some Complex integral forms , that need to be memorized thank you :

    Int 1/(sec x)
    int 1/(1+x^2)
    int tan x
    int cot x
    int 1/2x

    and a quick note on int of exponential functions ,


    thanks
    1. \int{\frac{1}{\sec{x}}\,dx} = \int{\cos{x}\,dx}.

    That's an easy one.


    2. \int{\frac{1}{1 + x^2}\,dx}.

    For this one use a substitution x = \tan{\theta}, making note that dx = \sec^2{\theta}\,d\theta.

    Also note that \theta = \arctan{x}.


    3. \int{\tan{x}\,dx} = \int{\frac{\sin{x}}{\cos{x}}\,dx}.

    Now use the substitution u = \cos{x}.


    4. \int{\cot{x}\,dx} = \int{\frac{\cos{x}}{\sin{x}}\,dx}.

    Now use the substitution u = \sin{x}.


    5. I can't tell if that's \int{\frac{1}{2x}\,dx} or \int{\frac{1}{2}x\,dx}.
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