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Resolución de integrales/ 3*x+1/ (3*x+10)/(x^2-8*x+10)

Integral de (3*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                 
  /                 
 |                  
 |     3*x + 10     
 |  ------------- dx
 |   2              
 |  x  - 8*x + 10   
 |                  
/                   
0
∫013x+10(x2−8x)+10 dx\int\limits_{0}^{1} \frac{3 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx 
Integral((3*x + 10)/(x^2 - 8*x + 10), (x, 0, 1))
Respuesta (Indefinida) [src] 
                             //            /  ___         \                    \                       
                             ||   ___      |\/ 6 *(-4 + x)|                    |                       
                             ||-\/ 6 *acoth|--------------|                    |                       
  /                          ||            \      6       /               2    |                       
 |                           ||-----------------------------  for (-4 + x)  > 6|        /      2      \
 |    3*x + 10               ||              6                                 |   3*log\10 + x  - 8*x/
 | ------------- dx = C + 22*|<                                                | + --------------------
 |  2                        ||            /  ___         \                    |            2          
 | x  - 8*x + 10             ||   ___      |\/ 6 *(-4 + x)|                    |                       
 |                           ||-\/ 6 *atanh|--------------|                    |                       
/                            ||            \      6       /               2    |                       
                             ||-----------------------------  for (-4 + x)  < 6|                       
                             \\              6                                 /
∫3x+10(x2−8x)+10 dx=C+22({−6acoth⁡(6(x−4)6)6for (x−4)2>6−6atanh⁡(6(x−4)6)6for (x−4)2<6)+3log⁡(x2−8x+10)2\int \frac{3 x + 10}{\left(x^{2} - 8 x\right) + 10}\, dx = C + 22 \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) + \frac{3 \log{\left(x^{2} - 8 x + 10 \right)}}{2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9005
Trazar el gráfico f(x)
Respuesta [src] 
/         ___\                           /         ___\                           /         ___\                           /         ___\                        
|3   11*\/ 6 | /          /      ___\\   |3   11*\/ 6 | /          /      ___\\   |3   11*\/ 6 | /          /      ___\\   |3   11*\/ 6 | /          /      ___\\
|- - --------|*\pi*I + log\3 - \/ 6 // + |- + --------|*\pi*I + log\3 + \/ 6 // - |- - --------|*\pi*I + log\4 - \/ 6 // - |- + --------|*\pi*I + log\4 + \/ 6 //
\2      6    /                           \2      6    /                           \2      6    /                           \2      6    /
−(32+1166)(log⁡(6+4)+iπ)+(32−1166)(log⁡(3−6)+iπ)−(32−1166)(log⁡(4−6)+iπ)+(32+1166)(log⁡(6+3)+iπ)- \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right) 
=
= 
/         ___\                           /         ___\                           /         ___\                           /         ___\                        
|3   11*\/ 6 | /          /      ___\\   |3   11*\/ 6 | /          /      ___\\   |3   11*\/ 6 | /          /      ___\\   |3   11*\/ 6 | /          /      ___\\
|- - --------|*\pi*I + log\3 - \/ 6 // + |- + --------|*\pi*I + log\3 + \/ 6 // - |- - --------|*\pi*I + log\4 - \/ 6 // - |- + --------|*\pi*I + log\4 + \/ 6 //
\2      6    /                           \2      6    /                           \2      6    /                           \2      6    /
−(32+1166)(log⁡(6+4)+iπ)+(32−1166)(log⁡(3−6)+iπ)−(32−1166)(log⁡(4−6)+iπ)+(32+1166)(log⁡(6+3)+iπ)- \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 4 \right)} + i \pi\right) + \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(3 - \sqrt{6} \right)} + i \pi\right) - \left(\frac{3}{2} - \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(4 - \sqrt{6} \right)} + i \pi\right) + \left(\frac{3}{2} + \frac{11 \sqrt{6}}{6}\right) \left(\log{\left(\sqrt{6} + 3 \right)} + i \pi\right) 
(3/2 - 11*sqrt(6)/6)*(pi*i + log(3 - sqrt(6))) + (3/2 + 11*sqrt(6)/6)*(pi*i + log(3 + sqrt(6))) - (3/2 - 11*sqrt(6)/6)*(pi*i + log(4 - sqrt(6))) - (3/2 + 11*sqrt(6)/6)*(pi*i + log(4 + sqrt(6)))
Respuesta numérica [src] 
2.08757087237553
2.08757087237553

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

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