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Identical expressions
sqrt(4x- five)
square root of (4x minus 5)
square root of (4x minus five)
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sqrt4x-5
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Solving integrals/ sqrt(4x-5)

Integral of sqrt(4x-5) dx

The solution

You have entered [src]

  1               
  /               
 |                
 |    _________   
 |  \/ 4*x - 5  dx
 |                
/                 
0

$$\int\limits_{0}^{1} \sqrt{4 x - 5}\, dx$$

Integral(sqrt(4*x - 5), (x, 0, 1))

Detail solution

Let $u = 4 x - 5$ .

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

$\int \frac{\sqrt{u}}{4}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \sqrt{u}\, du = \frac{\int \sqrt{u}\, du}{4}$
  1. The integral of $u^{n}$ is $\frac{u^{n + 1}}{n + 1}$ when $n \neq -1$ :
    
    $\int \sqrt{u}\, du = \frac{2 u^{\frac{3}{2}}}{3}$
  So, the result is: $\frac{u^{\frac{3}{2}}}{6}$
Now substitute $u$ back in:

$\frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}$
Now simplify:

$\frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}$
Add the constant of integration:

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

The answer is:

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

The answer (Indefinite) [src]

  /                                 
 |                               3/2
 |   _________          (4*x - 5)   
 | \/ 4*x - 5  dx = C + ------------
 |                           6      
/

$$\int \sqrt{4 x - 5}\, dx = C + \frac{\left(4 x - 5\right)^{\frac{3}{2}}}{6}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

            ___
  I   5*I*\/ 5 
- - + ---------
  6       6

$$- \frac{i}{6} + \frac{5 \sqrt{5} i}{6}$$

            ___
  I   5*I*\/ 5 
- - + ---------
  6       6

$$- \frac{i}{6} + \frac{5 \sqrt{5} i}{6}$$

-i/6 + 5*i*sqrt(5)/6

Numerical answer [src]

(0.0 + 1.69672331458316j)

(0.0 + 1.69672331458316j)

The graph

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

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Identical expressions

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Integral of sqrt(4x-5) dx

Limits of integration:

The graph:

Piecewise:

The solution