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C4 integration!!

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    Integrating using trig identities.

    I came across this example in my book...

     \int sin^2x  dx which is replaced by  \int \frac{1}{2}(1-cos2x) dx
    the result is then  \frac{1}{2}(x-\frac{1}{2}sin2x) + C
    I don't understand why it is only the bit in the brackets from  \int \frac{1}{2}(1-cos2x) dx that gets integrated?
    Is there a step inbetween where  \frac{1}{2} is moved before the integral sign? e.g.  \frac{1}{2} \int (1-cos2x) dx ?

    Any help is much appreciated!!
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    (Original post by icouldsay)
    Integrating using trig identities.

    I came across this example in my book...

     \int sin^2x  dx which is replaced by  \int \frac{1}{2}(1-cos2x) dx
    the result is then  \frac{1}{2}(x-\frac{1}{2}sin2x) + C
    I don't understand why it is only the bit in the brackets from  \int \frac{1}{2}(1-cos2x) dx that gets integrated?
    Is there a step inbetween where  \frac{1}{2} is moved before the integral sign? e.g.  \frac{1}{2} \int (1-cos2x) dx ?

    Any help is much appreciated!!
    Yep - 1/2 is a constant so you can move it outside.
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    Thank you!!

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