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Math Help - check integral is correct?

  1. #1
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    check integral is correct?

    could someone check ive done this right.... many thnaks

    evaluate

    <br /> <br />
\int {sin (4x)}{cos (x)} dx<br />

    i have....

    \int\frac{1}{2} {sin (a+b)}{sin (a-b)} dx<br />

    \int\frac{1}{2} {sin (5x)}{sin (3x)} dx<br />

    \int\frac{1}{2}\frac {(-cos (5x))}{5}+cos (3x)+c  dx<br />
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  2. #2
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    Quote Originally Posted by decoy808 View Post
    could someone check ive done this right.... many thnaks

    evaluate

    <br /> <br />
\int {sin (4x)}{cos (x)} dx<br />

    i have....

    \int\frac{1}{2} {sin (a+b)}{sin (a-b)} dx<br />

    \int\frac{1}{2} {sin (5x)}{sin (3x)} dx<br />

    \int\frac{1}{2}\frac {(-cos (5x))}{5}+cos (3x)+c dx<br />
    Check it here: integrate Sin&#x5b;4x&#x5d; Cos&#x5b;x&#x5d; - Wolfram|Alpha

    Click on Show steps.
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  3. #3
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    Quote Originally Posted by decoy808 View Post
    could someone check ive done this right.... many thnaks

    evaluate

    <br /> <br />
\int {sin (4x)}{cos (x)} dx<br />

    i have....

    \int\frac{1}{2}\left( {sin (a+b)}\color{red}+\color{black}{sin (a-b)}\right) dx<br />

    \int\frac{1}{2}\left( {sin (5x)}\color{red}+\color{black}{sin (3x)}\right) dx<br />

    \color{red}\int\color{black}\frac{1}{2}\frac {(-cos (5x))}{5}\color{red}+cos (3x)\color{black}+c  \color{red}dx<br />
    On your last line, you've integrated the first Sine correctly but not the second one, while not removing the integration and dx symbols
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