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Math Help - Integral Algebra

  1. #1
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    Integral Algebra

    Can someone please tell me why I have a +5 and +3 in the third step?


    \int[5x^2-6x-5 + \frac{10x+3}{x^2+1}]dx
    <br />
5 *\frac{1}{3}x^3-6*\frac{1}{2}x^2-5x+\int\frac{10x+3}{x^2+1}dx<br /> <br />
    <br />
\frac{5}{3}x^3-3x^2-5x+5\int\frac{10x}{x^2+1}+3\int\frac{3}{x^2+1}dx
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by gammaman View Post
    Can someone please tell me why I have a +5 and +3 in the third step?


    \int[5x^2-6x-5 + \frac{10x+3}{x^2+1}]dx
    <br />
5 *\frac{1}{3}x^3-6*\frac{1}{2}x^2-5x+\int\frac{10x+3}{x^2+1}dx<br /> <br />
    <br />
\frac{5}{3}x^3-3x^2-5x+5\int\frac{10x}{x^2+1}+3\int\frac{3}{x^2+1}dx
    They shouldn't be there...

    If you meant to write <br />
\frac{5}{3}x^3-3x^2-5x+5\int\frac{{\color{red}2}x}{x^2+1}+3\int\frac{{  \color{red}1}}{x^2+1}dx, then they should be there.
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  3. #3
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    Krizalid's Avatar
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    It's wrong.
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  4. #4
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    Thanks for confirming my suspecision. I thought that it was wrong unless I put it there and then reduce.
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  5. #5
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    Quote Originally Posted by Chris L T521 View Post

    If you meant to write <br />
\frac{5}{3}x^3-3x^2-5x+5\int\frac{{\color{red}2}x}{x^2+1}+3\int\frac{{  \color{red}1}}{x^2+1}dx, then they should be there.

    Did I integrate wrong?
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by gammaman View Post
    Did I integrate wrong?
    No. All I was saying was that the 5 and 3 you had in the 3rd line of your post shouldn't be there. However, I was pointing out that \int\frac{10x}{x^2+1}\,dx=5\int\frac{2x}{x^2+1}\,d  x and \int\frac{3}{x^2+1}\,dx=3\int\frac{1}{x^2+1}\,dx which would then imply \int\frac{10x+3}{x^2+1}\,dx=\int\frac{10x}{x^2+1}\  ,dx+\int\frac{3}{x^2+1}\,dx=5\int\frac{2x}{x^2+1}\  ,dx+3\int\frac{1}{x^2+1}\,dx
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  7. #7
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    Thanks, I agree. I just wanted to make sure I wasn't going crazy
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