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Resolución de integrales/ 4*x+1/ (4*x+10)/(x^2-8*x+10)

Integral de (4*x+10)/(x^2-8*x+10) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     4*x + 10     
 |  ------------- dx
 |   2              
 |  x  - 8*x + 10   
 |                  
/                   
0
∫014x+10(x2−8x)+10 dx\int\limits_{0}^{1} \frac{4 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx 
Integral((4*x + 10)/(x^2 - 8*x + 10), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                    //            /  ___         \                    \
                                                    ||   ___      |\/ 6 *(-4 + x)|                    |
                                                    ||-\/ 6 *acoth|--------------|                    |
  /                                                 ||            \      6       /               2    |
 |                                                  ||-----------------------------  for (-4 + x)  > 6|
 |    4*x + 10                 /      2      \      ||              6                                 |
 | ------------- dx = C + 2*log\10 + x  - 8*x/ + 26*|<                                                |
 |  2                                               ||            /  ___         \                    |
 | x  - 8*x + 10                                    ||   ___      |\/ 6 *(-4 + x)|                    |
 |                                                  ||-\/ 6 *atanh|--------------|                    |
/                                                   ||            \      6       /               2    |
                                                    ||-----------------------------  for (-4 + x)  < 6|
                                                    \\              6                                 /
∫4x+10(x2−8x)+10 dx=C+26({−6acoth⁡(6(x−4)6)6for (x−4)2>6−6atanh⁡(6(x−4)6)6for (x−4)2<6)+2log⁡(x2−8x+10)\int \frac{4 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx = C + 26 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 4\right)}{6} \right)}}{6} & \text{for}\: \left(x - 4\right)^{2} > 6 \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 4\right)}{6} \right)}}{6} & \text{for}\: \left(x - 4\right)^{2} < 6 \end{cases}\right) + 2 \log{\left(x^{2} - 8 x + 10 \right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9005
Trazar el gráfico f(x)
Respuesta [src] 
/         ___\                           /         ___\                           /         ___\                           /         ___\                        
|    13*\/ 6 | /          /      ___\\   |    13*\/ 6 | /          /      ___\\   |    13*\/ 6 | /          /      ___\\   |    13*\/ 6 | /          /      ___\\
|2 - --------|*\pi*I + log\3 - \/ 6 // + |2 + --------|*\pi*I + log\3 + \/ 6 // - |2 - --------|*\pi*I + log\4 - \/ 6 // - |2 + --------|*\pi*I + log\4 + \/ 6 //
\       6    /                           \       6    /                           \       6    /                           \       6    /
−(2+1366)(log⁡(6+4)+iπ)+(2−1366)(log⁡(3−6)+iπ)−(2−1366)(log⁡(4−6)+iπ)+(2+1366)(log⁡(6+3)+iπ)- \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right) 
=
= 
/         ___\                           /         ___\                           /         ___\                           /         ___\                        
|    13*\/ 6 | /          /      ___\\   |    13*\/ 6 | /          /      ___\\   |    13*\/ 6 | /          /      ___\\   |    13*\/ 6 | /          /      ___\\
|2 - --------|*\pi*I + log\3 - \/ 6 // + |2 + --------|*\pi*I + log\3 + \/ 6 // - |2 - --------|*\pi*I + log\4 - \/ 6 // - |2 + --------|*\pi*I + log\4 + \/ 6 //
\       6    /                           \       6    /                           \       6    /                           \       6    /
−(2+1366)(log⁡(6+4)+iπ)+(2−1366)(log⁡(3−6)+iπ)−(2−1366)(log⁡(4−6)+iπ)+(2+1366)(log⁡(6+3)+iπ)- \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(2 - \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(2 + \frac{13 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right) 
(2 - 13*sqrt(6)/6)*(pi*i + log(3 - sqrt(6))) + (2 + 13*sqrt(6)/6)*(pi*i + log(3 + sqrt(6))) - (2 - 13*sqrt(6)/6)*(pi*i + log(4 - sqrt(6))) - (2 + 13*sqrt(6)/6)*(pi*i + log(4 + sqrt(6)))
Respuesta numérica [src] 
2.1934990300061
2.1934990300061

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

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