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Solving integrals/ dx/(2x-1)(2x+3)

Integral of dx/(2x-1)(2x+3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   ___          
 \/ 3           
   /            
  |             
  |   2*x + 3   
  |   ------- dx
  |   2*x - 1   
  |             
 /              
  ___           
\/ 3            
-----           
  3
∫3332x+32x−1 dx\int\limits_{\frac{\sqrt{3}}{3}}^{\sqrt{3}} \frac{2 x + 3}{2 x - 1}\, dx 
Integral((2*x + 3)/(2*x - 1), (x, sqrt(3)/3, sqrt(3)))
The answer (Indefinite) [src] 
  /                                    
 |                                     
 | 2*x + 3                             
 | ------- dx = C + x + 2*log(-1 + 2*x)
 | 2*x - 1                             
 |                                     
/
∫2x+32x−1 dx=C+x+2log⁡(2x−1)\int \frac{2 x + 3}{2 x - 1}\, dx = C + x + 2 \log{\left(2 x - 1 \right)}
Simplify
The graph
0.60.70.80.91.01.11.21.31.41.51.61.7-5050
Plot the graph f(x)
The answer [src] 
       /         ___\                             ___
       |     2*\/ 3 |        /         ___\   2*\/ 3 
- 2*log|-1 + -------| + 2*log\-1 + 2*\/ 3 / + -------
       \        3   /                            3
233+2log⁡(−1+23)−2log⁡(−1+233)\frac{2 \sqrt{3}}{3} + 2 \log{\left(-1 + 2 \sqrt{3} \right)} - 2 \log{\left(-1 + \frac{2 \sqrt{3}}{3} \right)} 
=
= 
       /         ___\                             ___
       |     2*\/ 3 |        /         ___\   2*\/ 3 
- 2*log|-1 + -------| + 2*log\-1 + 2*\/ 3 / + -------
       \        3   /                            3
233+2log⁡(−1+23)−2log⁡(−1+233)\frac{2 \sqrt{3}}{3} + 2 \log{\left(-1 + 2 \sqrt{3} \right)} - 2 \log{\left(-1 + \frac{2 \sqrt{3}}{3} \right)} 
-2*log(-1 + 2*sqrt(3)/3) + 2*log(-1 + 2*sqrt(3)) + 2*sqrt(3)/3
Numerical answer [src] 
6.69088319035846
6.69088319035846

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

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