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Integral of (1/x+2/(x-1))dx dx

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The solution

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01(2x1+1x)dx\int\limits_{0}^{1} \left(\frac{2}{x - 1} + \frac{1}{x}\right)\, dx
Integral(1/x + 2/(x - 1), (x, 0, 1))
Detail solution
  1. Integrate term-by-term:

    1. The integral of a constant times a function is the constant times the integral of the function:

      2x1dx=21x1dx\int \frac{2}{x - 1}\, dx = 2 \int \frac{1}{x - 1}\, dx

      1. Let u=x1u = x - 1.

        Then let du=dxdu = dx and substitute dudu:

        1udu\int \frac{1}{u}\, du

        1. The integral of 1u\frac{1}{u} is log(u)\log{\left(u \right)}.

        Now substitute uu back in:

        log(x1)\log{\left(x - 1 \right)}

      So, the result is: 2log(x1)2 \log{\left(x - 1 \right)}

    1. The integral of 1x\frac{1}{x} is log(x)\log{\left(x \right)}.

    The result is: log(x)+2log(x1)\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}

  2. Now simplify:

    log(x)+2log(x1)\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}

  3. Add the constant of integration:

    log(x)+2log(x1)+constant\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}+ \mathrm{constant}


The answer is:

log(x)+2log(x1)+constant\log{\left(x \right)} + 2 \log{\left(x - 1 \right)}+ \mathrm{constant}

The answer (Indefinite) [src]
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(2x1+1x)dx=C+log(x)+2log(x1)\int \left(\frac{2}{x - 1} + \frac{1}{x}\right)\, dx = C + \log{\left(x \right)} + 2 \log{\left(x - 1 \right)}
The graph
0.001.000.100.200.300.400.500.600.700.800.90-2000020000
The answer [src]
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Numerical answer [src]
-44.0914674384461
-44.0914674384461

    Use the examples entering the upper and lower limits of integration.