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sqrt(4x-5)
Solving integrals/ sqrt(4x-5)

Integral of sqrt(4x-5) dx

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |    _________   
 |  \/ 4*x - 5  dx
 |                
/                 
0
∫014x−5 dx\int\limits_{0}^{1} \sqrt{4 x - 5}\, dx 
Integral(sqrt(4*x - 5), (x, 0, 1))
Detail solution

  1. Let u=4x−5u = 4 x - 5.

    Then let du=4dxdu = 4 dx and substitute du4\frac{du}{4}:

    ∫u4 du\int \frac{\sqrt{u}}{4}\, du

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

      ∫u du=∫u du4\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{4}

      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: u326\frac{u^{\frac{3}{2}}}{6}

    Now substitute uu back in:

    (4x−5)326\frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}

  2. Now simplify:

    (4x−5)326\frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}

  3. Add the constant of integration:

    (4x−5)326+constant\frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}

The answer is:

(4x−5)326+constant\frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                                 
 |                               3/2
 |   _________          (4*x - 5)   
 | \/ 4*x - 5  dx = C + ------------
 |                           6      
/
∫4x−5 dx=C+(4x−5)326\int \sqrt{4 x - 5}\, dx = C + \frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}
Simplify
The graph
-0.010-0.008-0.006-0.004-0.0020.0100.0000.0020.0040.0060.0080.00
Plot the graph f(x)
The answer [src] 
            ___
  I   5*I*\/ 5 
- - + ---------
  6       6
−i6+55i6- \frac{i}{6} + \frac{5 \sqrt{5} i}{6} 
=
= 
            ___
  I   5*I*\/ 5 
- - + ---------
  6       6
−i6+55i6- \frac{i}{6} + \frac{5 \sqrt{5} i}{6} 
-i/6 + 5*i*sqrt(5)/6
Numerical answer [src] 
(0.0 + 1.69672331458316j)
(0.0 + 1.69672331458316j)
The graph
Integral of sqrt(4x-5) dx

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

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