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

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

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                     
  /                     
 |                      
 |        x - 1         
 |  ----------------- dx
 |  (2*x + 1)*(x - 3)   
 |                      
/                       
0
$$\int\limits_{0}^{1} \frac{x - 1}{\left(x - 3\right) \left(2 x + 1\right)}\, dx$$ 
Integral((x - 1)/(((2*x + 1)*(x - 3))), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                         
 |                                                          
 |       x - 1                2*log(-3 + x)   3*log(1 + 2*x)
 | ----------------- dx = C + ------------- + --------------
 | (2*x + 1)*(x - 3)                7               14      
 |                                                          
/
$$\int \frac{x - 1}{\left(x - 3\right) \left(2 x + 1\right)}\, dx = C + \frac{2 \log{\left(x - 3 \right)}}{7} + \frac{3 \log{\left(2 x + 1 \right)}}{14}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(2)   2*log(3)   3*log(3/2)
------ - -------- + ----------
  2         7           14
$$- \frac{2 \log{\left(3 \right)}}{7} + \frac{3 \log{\left(\frac{3}{2} \right)}}{14} + \frac{\log{\left(2 \right)}}{2}$$ 
=
= 
log(2)   2*log(3)   3*log(3/2)
------ - -------- + ----------
  2         7           14
$$- \frac{2 \log{\left(3 \right)}}{7} + \frac{3 \log{\left(\frac{3}{2} \right)}}{14} + \frac{\log{\left(2 \right)}}{2}$$ 
log(2)/2 - 2*log(3)/7 + 3*log(3/2)/14
Numerical answer [src] 
0.119569745255119
0.119569745255119

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

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