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Solving integrals/ ln((3x-1)/(5x+2))

Integral of ln((3x-1)/(5x+2)) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                
  /                
 |                 
 |     /3*x - 1\   
 |  log|-------| dx
 |     \5*x + 2/   
 |                 
/                  
0
$$\int\limits_{0}^{1} \log{\left(\frac{3 x - 1}{5 x + 2} \right)}\, dx$$ 
Integral(log((3*x - 1)/(5*x + 2)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                     
 |                                                                      
 |    /3*x - 1\          2*log(2 + 5*x)   log(-1 + 3*x)        /3*x - 1\
 | log|-------| dx = C - -------------- - ------------- + x*log|-------|
 |    \5*x + 2/                5                3              \5*x + 2/
 |                                                                      
/
$$\int \log{\left(\frac{3 x - 1}{5 x + 2} \right)}\, dx = C + x \log{\left(\frac{3 x - 1}{5 x + 2} \right)} - \frac{\log{\left(3 x - 1 \right)}}{3} - \frac{2 \log{\left(5 x + 2 \right)}}{5}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  2*log(7/5)   log(3)   log(2/3)   2*log(2/5)   pi*I           
- ---------- - ------ - -------- + ---------- + ---- + log(2/7)
      5          3         3           5         3
$$\log{\left(\frac{2}{7} \right)} + \frac{2 \log{\left(\frac{2}{5} \right)}}{5} - \frac{\log{\left(3 \right)}}{3} - \frac{2 \log{\left(\frac{7}{5} \right)}}{5} - \frac{\log{\left(\frac{2}{3} \right)}}{3} + \frac{i \pi}{3}$$ 
=
= 
  2*log(7/5)   log(3)   log(2/3)   2*log(2/5)   pi*I           
- ---------- - ------ - -------- + ---------- + ---- + log(2/7)
      5          3         3           5         3
$$\log{\left(\frac{2}{7} \right)} + \frac{2 \log{\left(\frac{2}{5} \right)}}{5} - \frac{\log{\left(3 \right)}}{3} - \frac{2 \log{\left(\frac{7}{5} \right)}}{5} - \frac{\log{\left(\frac{2}{3} \right)}}{3} + \frac{i \pi}{3}$$ 
-2*log(7/5)/5 - log(3)/3 - log(2/3)/3 + 2*log(2/5)/5 + pi*i/3 + log(2/7)
Numerical answer [src] 
(-2.01758394978084 + 1.02998797848403j)
(-2.01758394978084 + 1.02998797848403j)

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

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