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Thread: 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. $\displaystyle \int{\frac{1}{\sec{x}}\,dx} = \int{\cos{x}\,dx}$.

    That's an easy one.


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

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

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


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

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


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

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


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