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Identical expressions
dx/(sqrt(five)(x)- one)
dx divide by ( square root of (5)(x) minus 1)
dx divide by ( square root of (five)(x) minus one)
dx/(√(5)(x)-1)
dx/sqrt5x-1
dx divide by (sqrt(5)(x)-1)
Similar expressions
dx/(sqrt(5)(x)+1)

Integral of dx/(sqrt(5)(x)-1) dx

The solution

You have entered [src]

  2               
  /               
 |                
 |       1        
 |  ----------- dx
 |    ___         
 |  \/ 5 *x - 1   
 |                
/                 
1

$$\int\limits_{1}^{2} \frac{1}{\sqrt{5} x - 1}\, dx$$

Integral(1/(sqrt(5)*x - 1), (x, 1, 2))

Detail solution

Let $u = \sqrt{5} x - 1$ .

Then let $du = \sqrt{5} dx$ and substitute $\frac{\sqrt{5} du}{5}$ :

$\int \frac{\sqrt{5}}{5 u}\, du$
1. The integral of a constant times a function is the constant times the integral of the function:
  
  $\int \frac{1}{u}\, du = \frac{\sqrt{5} \int \frac{1}{u}\, du}{5}$
  1. The integral of $\frac{1}{u}$ is $\log{\left(u \right)}$ .
  So, the result is: $\frac{\sqrt{5} \log{\left(u \right)}}{5}$
Now substitute $u$ back in:

$\frac{\sqrt{5} \log{\left(\sqrt{5} x - 1 \right)}}{5}$
Now simplify:

$\frac{\sqrt{5} \log{\left(\sqrt{5} x - 1 \right)}}{5}$
Add the constant of integration:

$\frac{\sqrt{5} \log{\left(\sqrt{5} x - 1 \right)}}{5}+ \mathrm{constant}$

The answer is:

$\frac{\sqrt{5} \log{\left(\sqrt{5} x - 1 \right)}}{5}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                           
 |                        ___    /  ___      \
 |      1               \/ 5 *log\\/ 5 *x - 1/
 | ----------- dx = C + ----------------------
 |   ___                          5           
 | \/ 5 *x - 1                                
 |                                            
/

$$\int \frac{1}{\sqrt{5} x - 1}\, dx = C + \frac{\sqrt{5} \log{\left(\sqrt{5} x - 1 \right)}}{5}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    ___    /       ___\     ___    /         ___\
  \/ 5 *log\-1 + \/ 5 /   \/ 5 *log\-1 + 2*\/ 5 /
- --------------------- + -----------------------
            5                        5

$$- \frac{\sqrt{5} \log{\left(-1 + \sqrt{5} \right)}}{5} + \frac{\sqrt{5} \log{\left(-1 + 2 \sqrt{5} \right)}}{5}$$

    ___    /       ___\     ___    /         ___\
  \/ 5 *log\-1 + \/ 5 /   \/ 5 *log\-1 + 2*\/ 5 /
- --------------------- + -----------------------
            5                        5

$$- \frac{\sqrt{5} \log{\left(-1 + \sqrt{5} \right)}}{5} + \frac{\sqrt{5} \log{\left(-1 + 2 \sqrt{5} \right)}}{5}$$

-sqrt(5)*log(-1 + sqrt(5))/5 + sqrt(5)*log(-1 + 2*sqrt(5))/5

Numerical answer [src]

0.461897674162808

0.461897674162808

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

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Identical expressions

Similar expressions

Integral of dx/(sqrt(5)(x)-1) dx

Limits of integration:

The graph:

Piecewise:

The solution