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Math Help - [SOLVED] Simplifying/Factoring an equation

  1. #1
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    [SOLVED] Simplifying/Factoring an equation

    Hi All,

    I had the question to integrate \int x \sqrt{2x+1} dx I've done the calculus bits, but I'm having trouble simplifying/factoring the algebra bits it to the correct answer.

    My answer: \frac{1}{10}{{(2x+1)}^{5/2}}-\frac{1}{6}{{(2x+1)}^{3/2}} + c

    The simplified answer: \frac{1}{15}{{(2x+1)}^{3/2}}(3x-1) + c

    If anyone could show me the algebra steps to simplify it, or just give me a start of how to do it it would be much appreciated,

    Thanks in advance.
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  2. #2
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    Quote Originally Posted by Markus123 View Post
    Hi All,

    I had the question to integrate \int x \sqrt{2x+1} dx I've done the calculus bits, but I'm having trouble simplifying/factoring the algebra bits it to the correct answer.

    My answer: \frac{1}{10}{{(2x+1)}^{5/2}}-\frac{1}{6}{{(2x+1)}^{3/2}} + c

    The simplified answer: \frac{1}{15}{{(2x+1)}^{3/2}}(3x-1) + c
    If you use the index law to write (2x+1)^{5/2} = (2x+1)(2x+1)^{3/2}, then you get \tfrac{1}{10}{{(2x+1)}^{5/2}}-\tfrac{1}{6}{{(2x+1)}^{3/2}} + c = (2x+1)^{3/2}\bigl(\tfrac1{10}(2x+1) - \tfrac16\bigr) + c, and all you have to do is simplify the contents of that bracket.
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  3. #3
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    Great, thanks!
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