anonymous
  • anonymous
I am trying to integrate (6x)/(1+2x). Wolfram tells me that I'll have to do long division in the process. Why is that so? http://www.wolframalpha.com/input/?i=integrate+%286x%29%2F%281%2B2x%29
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I think this is a simple u-substitution problem... you wanna work it?
anonymous
  • anonymous
oh, but answer to your question? because that's one way to do it?
anonymous
  • anonymous
I can take 6 out of the integral. Then, I will take (1+2x) as u and so 2 dx will be du. After that, I'll be left with this. Now?\[3\int\limits_{}^{}x/u \]What do I now?

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anonymous
  • anonymous
|dw:1332925190172:dw| |dw:1332925419347:dw|
anonymous
  • anonymous
can you take it from here?
anonymous
  • anonymous
Could it be done in this way? integral (6x)/(1+2x) dx =integral (3(1+2x)-3)/(1+2x) dx =integral ((3(1+2x)/(1+2x))-(3/(1+2x))) dx =integral (3)dx - integral(3/(1+2x))dx =3x-3 integral (1/(1+2x))dx =3x-3*(1/2) integral (1/(1+2x)) d(1+2x) =\[3x-(3/2) \ln \left| 1+2x \right|\]+C where C is a constant
anonymous
  • anonymous
@CoCoTsoi , that looks good too...
anonymous
  • anonymous
Thank you. :D
anonymous
  • anonymous
Sorry for replying so late. That helped immensely. Thanks a lot both of you. :)

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