Sr Examen

Otras calculadoras

Resolución de integrales/ x^2-4/ (3x+1)/ (3x+1)/(x^2-4x-2)

Integral de (3x+1)/(x^2-4x-2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                
  /                
 |                 
 |    3*x + 1      
 |  ------------ dx
 |   2             
 |  x  - 4*x - 2   
 |                 
/                  
0
∫013x+1(x2−4x)−2 dx\int\limits_{0}^{1} \frac{3 x + 1}{\left(x^{2} - 4 x\right) - 2}\, dx 
Integral((3*x + 1)/(x^2 - 4*x - 2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                           //            /  ___         \                    \                       
                           ||   ___      |\/ 6 *(-2 + x)|                    |                       
                           ||-\/ 6 *acoth|--------------|                    |                       
  /                        ||            \      6       /               2    |                       
 |                         ||-----------------------------  for (-2 + x)  > 6|        /      2      \
 |   3*x + 1               ||              6                                 |   3*log\-2 + x  - 4*x/
 | ------------ dx = C + 7*|<                                                | + --------------------
 |  2                      ||            /  ___         \                    |            2          
 | x  - 4*x - 2            ||   ___      |\/ 6 *(-2 + x)|                    |                       
 |                         ||-\/ 6 *atanh|--------------|                    |                       
/                          ||            \      6       /               2    |                       
                           ||-----------------------------  for (-2 + x)  < 6|                       
                           \\              6                                 /
∫3x+1(x2−4x)−2 dx=C+7({−6acoth⁡(6(x−2)6)6for (x−2)2>6−6atanh⁡(6(x−2)6)6for (x−2)2<6)+3log⁡(x2−4x−2)2\int \frac{3 x + 1}{\left(x^{2} - 4 x\right) - 2}\, dx = C + 7 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 2\right)}{6} \right)}}{6} & \text{for}\: \left(x - 2\right)^{2} < 6 \end{cases}\right) + \frac{3 \log{\left(x^{2} - 4 x - 2 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1.00.0
Trazar el gráfico f(x)
Respuesta [src] 
/        ___\                   /        ___\                           /        ___\                   /        ___\                        
|3   7*\/ 6 |    /       ___\   |3   7*\/ 6 | /          /      ___\\   |3   7*\/ 6 |    /       ___\   |3   7*\/ 6 | /          /      ___\\
|- - -------|*log\-1 + \/ 6 / + |- + -------|*\pi*I + log\1 + \/ 6 // - |- - -------|*log\-2 + \/ 6 / - |- + -------|*\pi*I + log\2 + \/ 6 //
\2      12  /                   \2      12  /                           \2      12  /                   \2      12  /
(32−7612)log⁡(−1+6)−(32−7612)log⁡(−2+6)−(7612+32)(log⁡(2+6)+iπ)+(7612+32)(log⁡(1+6)+iπ)\left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-2 + \sqrt{6} \right)} - \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) 
=
= 
/        ___\                   /        ___\                           /        ___\                   /        ___\                        
|3   7*\/ 6 |    /       ___\   |3   7*\/ 6 | /          /      ___\\   |3   7*\/ 6 |    /       ___\   |3   7*\/ 6 | /          /      ___\\
|- - -------|*log\-1 + \/ 6 / + |- + -------|*\pi*I + log\1 + \/ 6 // - |- - -------|*log\-2 + \/ 6 / - |- + -------|*\pi*I + log\2 + \/ 6 //
\2      12  /                   \2      12  /                           \2      12  /                   \2      12  /
(32−7612)log⁡(−1+6)−(32−7612)log⁡(−2+6)−(7612+32)(log⁡(2+6)+iπ)+(7612+32)(log⁡(1+6)+iπ)\left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-1 + \sqrt{6} \right)} - \left(\frac{3}{2} - \frac{7 \sqrt{6}}{12}\right) \log{\left(-2 + \sqrt{6} \right)} - \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(2 + \sqrt{6} \right)} + i \pi\right) + \left(\frac{7 \sqrt{6}}{12} + \frac{3}{2}\right) \left(\log{\left(1 + \sqrt{6} \right)} + i \pi\right) 
(3/2 - 7*sqrt(6)/12)*log(-1 + sqrt(6)) + (3/2 + 7*sqrt(6)/12)*(pi*i + log(1 + sqrt(6))) - (3/2 - 7*sqrt(6)/12)*log(-2 + sqrt(6)) - (3/2 + 7*sqrt(6)/12)*(pi*i + log(2 + sqrt(6)))
Respuesta numérica [src] 
-0.662298007912578
-0.662298007912578

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

    © Sr Examen – Калькулятор