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Resolución de integrales/ x^2-1/ 12x+1/ (3x-5)/ (3x-5)/(2x^2-12x+15)

Integral de (3x-5)/(2x^2-12x+15) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                    
  /                    
 |                     
 |      3*x - 5        
 |  ---------------- dx
 |     2               
 |  2*x  - 12*x + 15   
 |                     
/                      
0
∫013x−5(2x2−12x)+15 dx\int\limits_{0}^{1} \frac{3 x - 5}{\left(2 x^{2} - 12 x\right) + 15}\, dx 
Integral((3*x - 5)/(2*x^2 - 12*x + 15), (x, 0, 1))
Respuesta (Indefinida) [src] 
                               //            /  ___         \                      \                          
                               ||   ___      |\/ 6 *(-3 + x)|                      |                          
                               ||-\/ 6 *acoth|--------------|                      |                          
  /                            ||            \      3       /               2      |                          
 |                             ||-----------------------------  for (-3 + x)  > 3/2|        /               2\
 |     3*x - 5                 ||              6                                   |   3*log\15 - 12*x + 2*x /
 | ---------------- dx = C + 4*|<                                                  | + -----------------------
 |    2                        ||            /  ___         \                      |              4           
 | 2*x  - 12*x + 15            ||   ___      |\/ 6 *(-3 + x)|                      |                          
 |                             ||-\/ 6 *atanh|--------------|                      |                          
/                              ||            \      3       /               2      |                          
                               ||-----------------------------  for (-3 + x)  < 3/2|                          
                               \\              6                                   /
∫3x−5(2x2−12x)+15 dx=C+4({−6acoth⁡(6(x−3)3)6for (x−3)2>32−6atanh⁡(6(x−3)3)6for (x−3)2<32)+3log⁡(2x2−12x+15)4\int \frac{3 x - 5}{\left(2 x^{2} - 12 x\right) + 15}\, dx = C + 4 \left(\begin{cases} - \frac{\sqrt{6} \operatorname{acoth}{\left(\frac{\sqrt{6} \left(x - 3\right)}{3} \right)}}{6} & \text{for}\: \left(x - 3\right)^{2} > \frac{3}{2} \\- \frac{\sqrt{6} \operatorname{atanh}{\left(\frac{\sqrt{6} \left(x - 3\right)}{3} \right)}}{6} & \text{for}\: \left(x - 3\right)^{2} < \frac{3}{2} \end{cases}\right) + \frac{3 \log{\left(2 x^{2} - 12 x + 15 \right)}}{4}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-0.45-0.30
Trazar el gráfico f(x)
Respuesta [src] 
/      ___\ /          /      ___\\   /      ___\ /          /      ___\\   /      ___\ /          /      ___\\   /      ___\ /          /      ___\\
|3   \/ 6 | |          |    \/ 6 ||   |3   \/ 6 | |          |    \/ 6 ||   |3   \/ 6 | |          |    \/ 6 ||   |3   \/ 6 | |          |    \/ 6 ||
|- - -----|*|pi*I + log|2 - -----|| + |- + -----|*|pi*I + log|2 + -----|| - |- - -----|*|pi*I + log|3 - -----|| - |- + -----|*|pi*I + log|3 + -----||
\4     3  / \          \      2  //   \4     3  / \          \      2  //   \4     3  / \          \      2  //   \4     3  / \          \      2  //
−(34+63)(log⁡(62+3)+iπ)+(34−63)(log⁡(2−62)+iπ)−(34−63)(log⁡(3−62)+iπ)+(34+63)(log⁡(62+2)+iπ)- \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 3 \right)} + i \pi\right) + \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(2 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) - \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(3 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) + \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 2 \right)} + i \pi\right) 
=
= 
/      ___\ /          /      ___\\   /      ___\ /          /      ___\\   /      ___\ /          /      ___\\   /      ___\ /          /      ___\\
|3   \/ 6 | |          |    \/ 6 ||   |3   \/ 6 | |          |    \/ 6 ||   |3   \/ 6 | |          |    \/ 6 ||   |3   \/ 6 | |          |    \/ 6 ||
|- - -----|*|pi*I + log|2 - -----|| + |- + -----|*|pi*I + log|2 + -----|| - |- - -----|*|pi*I + log|3 - -----|| - |- + -----|*|pi*I + log|3 + -----||
\4     3  / \          \      2  //   \4     3  / \          \      2  //   \4     3  / \          \      2  //   \4     3  / \          \      2  //
−(34+63)(log⁡(62+3)+iπ)+(34−63)(log⁡(2−62)+iπ)−(34−63)(log⁡(3−62)+iπ)+(34+63)(log⁡(62+2)+iπ)- \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 3 \right)} + i \pi\right) + \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(2 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) - \left(\frac{3}{4} - \frac{\sqrt{6}}{3}\right) \left(\log{\left(3 - \frac{\sqrt{6}}{2} \right)} + i \pi\right) + \left(\frac{3}{4} + \frac{\sqrt{6}}{3}\right) \left(\log{\left(\frac{\sqrt{6}}{2} + 2 \right)} + i \pi\right) 
(3/4 - sqrt(6)/3)*(pi*i + log(2 - sqrt(6)/2)) + (3/4 + sqrt(6)/3)*(pi*i + log(2 + sqrt(6)/2)) - (3/4 - sqrt(6)/3)*(pi*i + log(3 - sqrt(6)/2)) - (3/4 + sqrt(6)/3)*(pi*i + log(3 + sqrt(6)/2))
Respuesta numérica [src] 
-0.36802571588101
-0.36802571588101

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

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