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Math Help - indeifinit integrals

  1. #1
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    indeifinit integrals

    Find the indefinite integral.

    ∫ (cos t) dt / (1 + sin t)





    The answer is:
    ln (1 + sin t) + C

    But i can't figure out the steps.
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  2. #2
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    Quote Originally Posted by corinna View Post
    Find the indefinite integral.

    ∫ (cos t) dt / (1 + sin t)





    The answer is:
    ln (1 + sin t) + C

    But i can't figure out the steps.
    Recognise that the numerator is the derivative of the denominator. Hence substituting u for the denominator would work:

     u = 1 + \sin(t)

     \frac{du}{dt} = \cos(t)

     du = \cos(t)dt

    Hence integral becomes:

     \int \frac{du}{u}
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