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

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

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1                  
  /                  
 |                   
 |        1          
 |  -------------- dx
 |     2             
 |  2*x  + 3*x - 1   
 |                   
/                    
0
∫011(2x2+3x)−1 dx\int\limits_{0}^{1} \frac{1}{\left(2 x^{2} + 3 x\right) - 1}\, dx 
Integral(1/(2*x^2 + 3*x - 1), (x, 0, 1))
The answer (Indefinite) [src] 
                             //             /    ____          \                      \
                             ||   ____      |4*\/ 17 *(3/4 + x)|                      |
                             ||-\/ 17 *acoth|------------------|                      |
  /                          ||             \        17        /                2   17|
 |                           ||----------------------------------  for (3/4 + x)  > --|
 |       1                   ||                68                                   16|
 | -------------- dx = C + 8*|<                                                       |
 |    2                      ||             /    ____          \                      |
 | 2*x  + 3*x - 1            ||   ____      |4*\/ 17 *(3/4 + x)|                      |
 |                           ||-\/ 17 *atanh|------------------|                      |
/                            ||             \        17        /                2   17|
                             ||----------------------------------  for (3/4 + x)  < --|
                             \\                68                                   16/
∫1(2x2+3x)−1 dx=C+8({−17acoth⁡(417(x+34)17)68for (x+34)2>1716−17atanh⁡(417(x+34)17)68for (x+34)2<1716)\int \frac{1}{\left(2 x^{2} + 3 x\right) - 1}\, dx = C + 8 \left(\begin{cases} - \frac{\sqrt{17} \operatorname{acoth}{\left(\frac{4 \sqrt{17} \left(x + \frac{3}{4}\right)}{17} \right)}}{68} & \text{for}\: \left(x + \frac{3}{4}\right)^{2} > \frac{17}{16} \\- \frac{\sqrt{17} \operatorname{atanh}{\left(\frac{4 \sqrt{17} \left(x + \frac{3}{4}\right)}{17} \right)}}{68} & \text{for}\: \left(x + \frac{3}{4}\right)^{2} < \frac{17}{16} \end{cases}\right)
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.90-1000010000
Plot the graph f(x)
The answer [src] 
nan
NaN\text{NaN} 
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= 
nan
NaN\text{NaN} 
nan
Numerical answer [src] 
-1.92938438445434
-1.92938438445434

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