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Math Help - Trig Integration

  1. #1
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    Trig Integration

    I have to integrate sin^2xcos^5x dx

    I've come to the answer of -t^6/6 +t^11/11 + C where t= cosx

    Im worried its incorrect
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  2. #2
    Bar0n janvdl's Avatar
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    Quote Originally Posted by qwerty10 View Post
    I have to integrate sin^2xcos^5x dx

    I've come to the answer of -t^6/6 +t^11/11 + C where t= cosx

    Im worried its incorrect
    If you ever need to check your integration, use Wolfram.

    Your integral.

    You can even ask it to show you the intermediate steps
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  3. #3
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    Using the identity \cos^2(x) = 1-\sin^2(x) and writing \cos^4(x) = (\cos^2(x))^2 the question can be rewritten as \sin^2(x)(1-\cos^2(x))^2\cos(x)

    Let u = \sin(x) so that du = \cos(x)\, dx \implies dx = \dfrac{du}{\cos(u)}

    Now putting our subs into the integral we get

    \int u^2(1-u^2)^2 du and expanding the brackets we get \int u^2(1-2u^2+u^4)\ du = \int u^2-2u^4+u^6\ du
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