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Resolución de integrales/ (2x-5)/ x^2-x/ (2x-5)/(2x^2-x-4)

Integral de (2x-5)/(2x^2-x-4) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    2*x - 5      
 |  ------------ dx
 |     2           
 |  2*x  - x - 4   
 |                 
/                  
0
∫012x−5(2x2−x)−4 dx\int\limits_{0}^{1} \frac{2 x - 5}{\left(2 x^{2} - x\right) - 4}\, dx 
Integral((2*x - 5)/(2*x^2 - x - 4), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                 //             /    ____           \                       \
                                                 ||   ____      |4*\/ 33 *(-1/4 + x)|                       |
                                                 ||-\/ 33 *acoth|-------------------|                       |
  /                                              ||             \         33        /                 2   33|
 |                          /            2\      ||-----------------------------------  for (-1/4 + x)  > --|
 |   2*x - 5             log\-4 - x + 2*x /      ||                132                                    16|
 | ------------ dx = C + ------------------ - 36*|<                                                         |
 |    2                          2               ||             /    ____           \                       |
 | 2*x  - x - 4                                  ||   ____      |4*\/ 33 *(-1/4 + x)|                       |
 |                                               ||-\/ 33 *atanh|-------------------|                       |
/                                                ||             \         33        /                 2   33|
                                                 ||-----------------------------------  for (-1/4 + x)  < --|
                                                 \\                132                                    16/
∫2x−5(2x2−x)−4 dx=C−36({−33acoth⁡(433(x−14)33)132for (x−14)2>3316−33atanh⁡(433(x−14)33)132for (x−14)2<3316)+log⁡(2x2−x−4)2\int \frac{2 x - 5}{\left(2 x^{2} - x\right) - 4}\, dx = C - 36 \left(\begin{cases} - \frac{\sqrt{33} \operatorname{acoth}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} > \frac{33}{16} \\- \frac{\sqrt{33} \operatorname{atanh}{\left(\frac{4 \sqrt{33} \left(x - \frac{1}{4}\right)}{33} \right)}}{132} & \text{for}\: \left(x - \frac{1}{4}\right)^{2} < \frac{33}{16} \end{cases}\right) + \frac{\log{\left(2 x^{2} - x - 4 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.900.51.5
Trazar el gráfico f(x)
Respuesta [src] 
/        ____\ /          /        ____\\   /        ____\    /      ____\   /        ____\ /          /      ____\\   /        ____\    /        ____\
|1   3*\/ 33 | |          |  3   \/ 33 ||   |1   3*\/ 33 |    |3   \/ 33 |   |1   3*\/ 33 | |          |1   \/ 33 ||   |1   3*\/ 33 |    |  1   \/ 33 |
|- - --------|*|pi*I + log|- - + ------|| + |- + --------|*log|- + ------| - |- - --------|*|pi*I + log|- + ------|| - |- + --------|*log|- - + ------|
\2      22   / \          \  4     4   //   \2      22   /    \4     4   /   \2      22   / \          \4     4   //   \2      22   /    \  4     4   /
−(12+33322)log⁡(−14+334)+(12+33322)log⁡(34+334)+(12−33322)(log⁡(−34+334)+iπ)−(12−33322)(log⁡(14+334)+iπ)- \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) - \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) 
=
= 
/        ____\ /          /        ____\\   /        ____\    /      ____\   /        ____\ /          /      ____\\   /        ____\    /        ____\
|1   3*\/ 33 | |          |  3   \/ 33 ||   |1   3*\/ 33 |    |3   \/ 33 |   |1   3*\/ 33 | |          |1   \/ 33 ||   |1   3*\/ 33 |    |  1   \/ 33 |
|- - --------|*|pi*I + log|- - + ------|| + |- + --------|*log|- + ------| - |- - --------|*|pi*I + log|- + ------|| - |- + --------|*log|- - + ------|
\2      22   / \          \  4     4   //   \2      22   /    \4     4   /   \2      22   / \          \4     4   //   \2      22   /    \  4     4   /
−(12+33322)log⁡(−14+334)+(12+33322)log⁡(34+334)+(12−33322)(log⁡(−34+334)+iπ)−(12−33322)(log⁡(14+334)+iπ)- \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(- \frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} + \frac{3 \sqrt{33}}{22}\right) \log{\left(\frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(- \frac{3}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) - \left(\frac{1}{2} - \frac{3 \sqrt{33}}{22}\right) \left(\log{\left(\frac{1}{4} + \frac{\sqrt{33}}{4} \right)} + i \pi\right) 
(1/2 - 3*sqrt(33)/22)*(pi*i + log(-3/4 + sqrt(33)/4)) + (1/2 + 3*sqrt(33)/22)*log(3/4 + sqrt(33)/4) - (1/2 - 3*sqrt(33)/22)*(pi*i + log(1/4 + sqrt(33)/4)) - (1/2 + 3*sqrt(33)/22)*log(-1/4 + sqrt(33)/4)
Respuesta numérica [src] 
1.03944571602599
1.03944571602599

    Estos ejemplos se pueden aplicar para introducción de los límites de integración inferior y superior.

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