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Math Help - substitution sin and cos

  1. #1
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    substitution sin and cos

    Hi

    I have the answer in the textbook for this one but I am hoping someone can explain it to me.

    integral sign (sin x/ (1+ cos^2 x) dx =
    integral sign ((sin x cos x)/(1+cos^2 x)dx

    why was cos x "added" to the numerator - it wasn't "added" to the denominator - it just seems to come out of no where.

    Any enlightenment would be appreciated.
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  2. #2
    Eater of Worlds
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    I don't know, but here is how you could integrate it. By making a u-sub.

    \int\frac{sin(x)}{1+cos^{2}(x)}dx

    Let u=cos(x), \;\ -du=sin(x)dx

    Now, can you finish?.
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