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Math Help - Integral with sub. method?

  1. #1
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    Integral with sub. method?

    Can someone explain how to use the substitution method to find the integral of:

    \int_{-1}^{1} \frac{2x + 1}{x^2 + x + 1}dx
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    Quote Originally Posted by wizzler View Post
    Can someone explain how to use the substitution method to find the integral of:

    \int_{-1}^{1} \frac{2x + 1}{x^2 + x + 1}dx
    Let t=x^2+x+1 then t'=2x+1.
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    Quote Originally Posted by ThePerfectHacker View Post
    Let t=x^2+x+1 then t'=2x+1.

    can you show me all the steps, i.e. the whole solution? I seem to get like \frac{t'}{t}
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    Quote Originally Posted by wizzler View Post
    can you show me all the steps, i.e. the whole solution? I seem to get like \frac{t'}{t}
    That's what you should get!

    \int \frac{t^{\prime}}{t}dt = ln|t| + C

    -Dan
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    Quote Originally Posted by topsquark View Post
    That's what you should get!

    \int \frac{t^{\prime}}{t}dt = ln|t| + C

    -Dan

    oh right.. so then i can just put in 3 and 1 for the function because if x = 1 then t = 3; if x = -1 then t = 1 so I get: (Note it's a definite integral!!!)

    ln(3) - ln(1) and that is the same as ln(\frac{3}{1}) = ln(3)

    correct or have I misunderstood something?
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by wizzler View Post
    oh right.. so then i can just put in 3 and 1 for the function because if x = 1 then t = 3; if x = -1 then t = 1 so I get: (Note it's a definite integral!!!)

    ln(3) - ln(1) and that is the same as ln(\frac{3}{1}) = ln(3)

    correct or have I misunderstood something?
    Yup.

    -Dan
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