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

Integral of 1/(2*x) dx

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The solution

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

  1. Let u=2xu = 2 x.

    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)2\frac{\log{\left(2 x \right)}}{2}

  2. Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src] 
  /                     
 |                      
 |  1           log(2*x)
 | --- dx = C + --------
 | 2*x             2    
 |                      
/
∫12x dx=C+log⁡(2x)2\int \frac{1}{2 x}\, dx = C + \frac{\log{\left(2 x \right)}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-50005000
Plot the graph f(x)
The answer [src] 
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∞\infty 
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∞\infty 
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Numerical answer [src] 
22.0452230669964
22.0452230669964
The graph
Integral of 1/(2*x) dx

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

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