Sr Examen

Otras calculadoras

Resolución de integrales/ x^2-x/ (1)/(x^2-x-1)

Integral de (1)/(x^2-x-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1              
  /              
 |               
 |      1        
 |  ---------- dx
 |   2           
 |  x  - x - 1   
 |               
/                
0
∫011(x2−x)−1 dx\int\limits_{0}^{1} \frac{1}{\left(x^{2} - x\right) - 1}\, dx 
Integral(1/(x^2 - x - 1), (x, 0, 1))
Respuesta (Indefinida) [src] 
                         //            /    ___           \                        \
                         ||   ___      |2*\/ 5 *(-1/2 + x)|                        |
                         ||-\/ 5 *acoth|------------------|                        |
  /                      ||            \        5         /                 2      |
 |                       ||---------------------------------  for (-1/2 + x)  > 5/4|
 |     1                 ||                10                                      |
 | ---------- dx = C + 4*|<                                                        |
 |  2                    ||            /    ___           \                        |
 | x  - x - 1            ||   ___      |2*\/ 5 *(-1/2 + x)|                        |
 |                       ||-\/ 5 *atanh|------------------|                        |
/                        ||            \        5         /                 2      |
                         ||---------------------------------  for (-1/2 + x)  < 5/4|
                         \\                10                                      /
∫1(x2−x)−1 dx=C+4({−5acoth⁡(25(x−12)5)10for (x−12)2>54−5atanh⁡(25(x−12)5)10for (x−12)2<54)\int \frac{1}{\left(x^{2} - x\right) - 1}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{5} \operatorname{acoth}{\left(\frac{2 \sqrt{5} \left(x - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(x - \frac{1}{2}\right)^{2} > \frac{5}{4} \\- \frac{\sqrt{5} \operatorname{atanh}{\left(\frac{2 \sqrt{5} \left(x - \frac{1}{2}\right)}{5} \right)}}{10} & \text{for}\: \left(x - \frac{1}{2}\right)^{2} < \frac{5}{4} \end{cases}\right)
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1.2-0.6
Trazar el gráfico f(x)
Respuesta [src] 
        /          /      ___\\            /      ___\         /          /        ___\\            /        ___\
    ___ |          |1   \/ 5 ||     ___    |1   \/ 5 |     ___ |          |  1   \/ 5 ||     ___    |  1   \/ 5 |
  \/ 5 *|pi*I + log|- + -----||   \/ 5 *log|- + -----|   \/ 5 *|pi*I + log|- - + -----||   \/ 5 *log|- - + -----|
        \          \2     2  //            \2     2  /         \          \  2     2  //            \  2     2  /
- ----------------------------- - -------------------- + ------------------------------- + ----------------------
                5                          5                            5                            5
−5log⁡(12+52)5+5log⁡(−12+52)5−5(log⁡(12+52)+iπ)5+5(log⁡(−12+52)+iπ)5- \frac{\sqrt{5} \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{5} + \frac{\sqrt{5} \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)}{5} 
=
= 
        /          /      ___\\            /      ___\         /          /        ___\\            /        ___\
    ___ |          |1   \/ 5 ||     ___    |1   \/ 5 |     ___ |          |  1   \/ 5 ||     ___    |  1   \/ 5 |
  \/ 5 *|pi*I + log|- + -----||   \/ 5 *log|- + -----|   \/ 5 *|pi*I + log|- - + -----||   \/ 5 *log|- - + -----|
        \          \2     2  //            \2     2  /         \          \  2     2  //            \  2     2  /
- ----------------------------- - -------------------- + ------------------------------- + ----------------------
                5                          5                            5                            5
−5log⁡(12+52)5+5log⁡(−12+52)5−5(log⁡(12+52)+iπ)5+5(log⁡(−12+52)+iπ)5- \frac{\sqrt{5} \log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{5} + \frac{\sqrt{5} \log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(\frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(- \frac{1}{2} + \frac{\sqrt{5}}{2} \right)} + i \pi\right)}{5} 
-sqrt(5)*(pi*i + log(1/2 + sqrt(5)/2))/5 - sqrt(5)*log(1/2 + sqrt(5)/2)/5 + sqrt(5)*(pi*i + log(-1/2 + sqrt(5)/2))/5 + sqrt(5)*log(-1/2 + sqrt(5)/2)/5
Respuesta numérica [src] 
-0.860817881928008
-0.860817881928008

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

    © Sr Examen – Калькулятор