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Integral of 1/(3*x-4*sqrt(x)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1                 
  /                 
 |                  
 |        1         
 |  ------------- dx
 |            ___   
 |  3*x - 4*\/ x    
 |                  
/                   
0                   
$$\int\limits_{0}^{1} \frac{1}{- 4 \sqrt{x} + 3 x}\, dx$$
Integral(1/(3*x - 4*sqrt(x)), (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

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

      1. Let .

        Then let and substitute :

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

          1. The integral of is .

          So, the result is:

        Now substitute back in:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                          
 |                             /         ___\
 |       1                2*log\-4 + 3*\/ x /
 | ------------- dx = C + -------------------
 |           ___                   3         
 | 3*x - 4*\/ x                              
 |                                           
/                                            
$$\int \frac{1}{- 4 \sqrt{x} + 3 x}\, dx = C + \frac{2 \log{\left(3 \sqrt{x} - 4 \right)}}{3}$$
The graph
The answer [src]
  2*log(3)   2*log(4/3)
- -------- - ----------
     3           3     
$$- \frac{2 \log{\left(3 \right)}}{3} - \frac{2 \log{\left(\frac{4}{3} \right)}}{3}$$
=
=
  2*log(3)   2*log(4/3)
- -------- - ----------
     3           3     
$$- \frac{2 \log{\left(3 \right)}}{3} - \frac{2 \log{\left(\frac{4}{3} \right)}}{3}$$
-2*log(3)/3 - 2*log(4/3)/3
Numerical answer [src]
-0.924196240579125
-0.924196240579125

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