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Integral of (x+√(2x+3))/(x-1) dx

Limits of integration:

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The solution

You have entered [src]
  1                   
  /                   
 |                    
 |        _________   
 |  x + \/ 2*x + 3    
 |  --------------- dx
 |       x - 1        
 |                    
/                     
0                     
$$\int\limits_{0}^{1} \frac{x + \sqrt{2 x + 3}}{x - 1}\, dx$$
Integral((x + sqrt(2*x + 3))/(x - 1), (x, 0, 1))
The answer (Indefinite) [src]
                                                       //            /  ___   _________\                  \                
                                                       ||   ___      |\/ 5 *\/ 2*x + 3 |                  |                
  /                                                    ||-\/ 5 *acoth|-----------------|                  |                
 |                                                     ||            \        5        /                  |                
 |       _________                                     ||--------------------------------  for 2*x + 3 > 5|                
 | x + \/ 2*x + 3       3               _________      ||               5                                 |                
 | --------------- dx = - + C + x + 2*\/ 2*x + 3  + 10*|<                                                 | + log(-2 + 2*x)
 |      x - 1           2                              ||            /  ___   _________\                  |                
 |                                                     ||   ___      |\/ 5 *\/ 2*x + 3 |                  |                
/                                                      ||-\/ 5 *atanh|-----------------|                  |                
                                                       ||            \        5        /                  |                
                                                       ||--------------------------------  for 2*x + 3 < 5|                
                                                       \\               5                                 /                
$$\int \frac{x + \sqrt{2 x + 3}}{x - 1}\, dx = C + x + 2 \sqrt{2 x + 3} + 10 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{\sqrt{5} \sqrt{2 x + 3}}{5} \right)}}{5} & \text{for}\: 2 x + 3 > 5 \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{\sqrt{5} \sqrt{2 x + 3}}{5} \right)}}{5} & \text{for}\: 2 x + 3 < 5 \end{cases}\right) + \log{\left(2 x - 2 \right)} + \frac{3}{2}$$
Numerical answer [src]
-141.208050251919
-141.208050251919

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