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Math Help - Indefinite Integral help

  1. #1
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    Indefinite Integral help

    I have this problem for homework:

    Evaluate the indefinite integral



    I don't know how to decide which numbers to pick as the 'u'. Is there a rule to follow, or do you just pick any one at random?

    Thank you
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  2. #2
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    Quote Originally Posted by JohnJames View Post
    I have this problem for homework:

    Evaluate the indefinite integral



    I don't know how to decide which numbers to pick as the 'u'. Is there a rule to follow, or do you just pick any one at random?

    Thank you

    \displaystyle \frac{1}{8} \int \frac{\cos{x}}{\sin{x}+6} \, dx

    u = \sin{x} + 6

    du = \cos{x} \, dx

    substitute, integrate, then back substitute ...

    \displaystyle \frac{1}{8} \int \frac{du}{u}

    \displaystyle \frac{1}{8} \ln{u} + C


    \displaystyle \frac{1}{8} \ln(\sin{x}+6) + C
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  3. #3
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    Thanks again for your help Skeeter, sorry for the late response.

    How did you get:



    I don't understand that part of it.
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  4. #4
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    you should already know the following general antiderivative ...

    \displaystyle \int \frac{dx}{x} = \ln|x| + C

    link ...

    Pauls Online Notes : Calculus I - Computing Indefinite Integrals
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  5. #5
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    Thanks so much Skeeter, you been a real big help man.
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