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1/(2x-1)
Solving integrals/ 1/(2x-1)

Integral of 1/(2x-1) dx

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The solution

You have entered [src] 
  1           
  /           
 |            
 |     1      
 |  ------- dx
 |  2*x - 1   
 |            
/             
0
∫0112x−1 dx\int\limits_{0}^{1} \frac{1}{2 x - 1}\, dx 
Integral(1/(2*x - 1), (x, 0, 1))
Detail solution

  1. Let u=2x−1u = 2 x - 1.

    Then let du=2dxdu = 2 dx and substitute du2\frac{du}{2}:

    ∫12u du\int \frac{1}{2 u}\, du

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

      ∫1u du=∫1u du2\int \frac{1}{u}\, du = \frac{\int \frac{1}{u}\, du}{2}

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

      So, the result is: log⁡(u)2\frac{\log{\left(u \right)}}{2}

    Now substitute uu back in:

    log⁡(2x−1)2\frac{\log{\left(2 x - 1 \right)}}{2}

  2. Now simplify:

    log⁡(2x−1)2\frac{\log{\left(2 x - 1 \right)}}{2}

  3. Add the constant of integration:

    log⁡(2x−1)2+constant\frac{\log{\left(2 x - 1 \right)}}{2}+ \mathrm{constant}

The answer is:

log⁡(2x−1)2+constant\frac{\log{\left(2 x - 1 \right)}}{2}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                              
 |    1             log(2*x - 1)
 | ------- dx = C + ------------
 | 2*x - 1               2      
 |                              
/
∫12x−1 dx=C+log⁡(2x−1)2\int \frac{1}{2 x - 1}\, dx = C + \frac{\log{\left(2 x - 1 \right)}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-5000050000
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The answer [src] 
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The graph
Integral of 1/(2x-1) dx

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

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