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Math Help - [SOLVED] Trigonometric integral

  1. #1
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    [SOLVED] Trigonometric integral

    How do you solve the following indefinite integral:

    <br />
\int {\sin^3 (2x)}{\sqrt{\cos (2x)}} dx<br />
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  2. #2
    Super Member Matt Westwood's Avatar
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    Quote Originally Posted by baseballman View Post
    How do you solve the following indefinite integral:

    <br />
\int {\sin^3 (2x)}{\sqrt{\cos (2x)}} dx<br />
    Have you tried a trig substitution? u = \sin (2x) or u = \cos (2x) or something?
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  3. #3
    MHF Contributor

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    Write the integral as \int sin^2(2x)\sqrt{cos(2x)}(sin(2x)dx)= \int (1- cos^2(2x)\sqrt{cos(2x)}(sin(2x)dx) and use the substitution u= cos(2x).
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  4. #4
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    Got this answer:

    <br />
\frac{1}<br />
{3}\sqrt {{{\cos }^3}(2x)} + \frac{1}<br />
{7}\sqrt {{{\cos }^7}(2x)} + C<br />

    Thanks for your quick response.
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