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(x-3)/(4x^2+2x-3)
Solving integrals/ (x-3)/(4x^2+2x-3)

Integral of (x-3)/(4x^2+2x-3) dx

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  1                  
  /                  
 |                   
 |      x - 3        
 |  -------------- dx
 |     2             
 |  4*x  + 2*x - 3   
 |                   
/                    
0
$$\int\limits_{0}^{1} \frac{x - 3}{\left(4 x^{2} + 2 x\right) - 3}\, dx$$ 
Integral((x - 3)/(4*x^2 + 2*x - 3), (x, 0, 1))
The answer (Indefinite) [src] 
                              //             /    ____          \                      \                       
                              ||   ____      |4*\/ 13 *(1/4 + x)|                      |                       
                              ||-\/ 13 *acoth|------------------|                      |                       
  /                           ||             \        13        /                2   13|                       
 |                            ||----------------------------------  for (1/4 + x)  > --|      /              2\
 |     x - 3                  ||                52                                   16|   log\-3 + 2*x + 4*x /
 | -------------- dx = C - 13*|<                                                       | + --------------------
 |    2                       ||             /    ____          \                      |            8          
 | 4*x  + 2*x - 3             ||   ____      |4*\/ 13 *(1/4 + x)|                      |                       
 |                            ||-\/ 13 *atanh|------------------|                      |                       
/                             ||             \        13        /                2   13|                       
                              ||----------------------------------  for (1/4 + x)  < --|                       
                              \\                52                                   16/
$$\int \frac{x - 3}{\left(4 x^{2} + 2 x\right) - 3}\, dx = C - 13 \left(\begin{cases} - \frac{\sqrt{13} \operatorname{acoth}{\left(\frac{4 \sqrt{13} \left(x + \frac{1}{4}\right)}{13} \right)}}{52} & \text{for}\: \left(x + \frac{1}{4}\right)^{2} > \frac{13}{16} \\- \frac{\sqrt{13} \operatorname{atanh}{\left(\frac{4 \sqrt{13} \left(x + \frac{1}{4}\right)}{13} \right)}}{52} & \text{for}\: \left(x + \frac{1}{4}\right)^{2} < \frac{13}{16} \end{cases}\right) + \frac{\log{\left(4 x^{2} + 2 x - 3 \right)}}{8}$$
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The answer [src] 
nan
$$\text{NaN}$$ 
=
= 
nan
$$\text{NaN}$$ 
nan
Numerical answer [src] 
0.0308948144541974
0.0308948144541974
The graph
Integral of (x-3)/(4x^2+2x-3) dx

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

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