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

Integral of sqrt(2x-1)dx dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |    _________   
 |  \/ 2*x - 1  dx
 |                
/                 
0
∫012x−1 dx\int\limits_{0}^{1} \sqrt{2 x - 1}\, dx 
Integral(sqrt(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}:

    ∫u2 du\int \frac{\sqrt{u}}{2}\, du

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

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

      1. The integral of unu^{n} is un+1n+1\frac{u^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫u du=2u323\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}

      So, the result is: u323\frac{u^{\frac{3}{2}}}{3}

    Now substitute uu back in:

    (2x−1)323\frac{\left(2 x - 1\right)^{\frac{3}{2}}}{3}

  2. Now simplify:

    (2x−1)323\frac{\left(2 x - 1\right)^{\frac{3}{2}}}{3}

  3. Add the constant of integration:

    (2x−1)323+constant\frac{\left(2 x - 1\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer is:

(2x−1)323+constant\frac{\left(2 x - 1\right)^{\frac{3}{2}}}{3}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                               3/2
 |   _________          (2*x - 1)   
 | \/ 2*x - 1  dx = C + ------------
 |                           3      
/
∫2x−1 dx=C+(2x−1)323\int \sqrt{2 x - 1}\, dx = C + \frac{\left(2 x - 1\right)^{\frac{3}{2}}}{3}
Simplify
The graph
1.000.500.550.600.650.700.750.800.850.900.9502
Plot the graph f(x)
The answer [src] 
1   I
- + -
3   3
13+i3\frac{1}{3} + \frac{i}{3} 
=
= 
1   I
- + -
3   3
13+i3\frac{1}{3} + \frac{i}{3} 
1/3 + i/3
Numerical answer [src] 
(0.332933650455812 + 0.332933650455812j)
(0.332933650455812 + 0.332933650455812j)
The graph
Integral of sqrt(2x-1)dx dx

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

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