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Math Help - integration

  1. #1
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    integration

    Hello,

    I am having trouble integrating the following equation, I thought I could do it but it is not the same as the answer in the back of the book. Can someone help me?

    The integral of (2x+3)/(x+1)dx thanks
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    Quote Originally Posted by jarny View Post
    Hello,

    I am having trouble integrating the following equation, I thought I could do it but it is not the same as the answer in the back of the book. Can someone help me?

    The integral of (2x+3)/(x+1)dx thanks
    \int\frac{2x+3}{x+1}\,dx

    =\int\frac{2x+2+1}{x+1}\,dx

    =\int\frac{2(x+1)+1}{x+1}\,dx

    =\int\left[\frac{2(x+1)}{x+1}+\frac1{x+1}\right]dx

    =\int\left(2+\frac1{x+1}\right)dx

    You could have also used polynomial long division.
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  3. #3
    Bar0n janvdl's Avatar
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    Quote Originally Posted by jarny View Post
    Hello,

    I am having trouble integrating the following equation, I thought I could do it but it is not the same as the answer in the back of the book. Can someone help me?

    The integral of (2x+3)/(x+1)dx thanks
    \int{\frac{2x+3}{x+1}} dx

    = 2 \int{ \frac{x}{x+1} }dx + 3 \int{ \frac{1}{x+1} }dx

    = 2 \int{ \frac{x+1-1}{x+1} }dx + 3 \ln{(x+1)} + C

    <br />
= 2 \left( \int{ \frac{x+1}{x+1} }dx + \int{ \frac{-1}{x+1} }dx \right) + 3 \ln{(x+1)} + C

    = 2 \left( \int{ 1 }dx + \int{ \frac{-1}{x+1} }dx \right) + 3 \ln{(x+1)} + C

    = 2 \left( x - \ln{(x+1)} \right) + 3 \ln{(x+1)} + C

    = 2x + \ln{(x+1)} + C
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  4. #4
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    Krizalid's Avatar
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    Of course janvdl meant to say \ln|x+1|.
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  5. #5
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    thanks a lot guys
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  6. #6
    Bar0n janvdl's Avatar
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    Quote Originally Posted by Krizalid View Post
    Of course janvdl meant to say \ln|x+1|.
    I even wrote it like that on the paper I worked it out on... Sorry about that.
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