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Resolución de integrales/ cos(x)/(cos^2(x)-5*cos(x)+6)

Integral de cos(x)/(cos^2(x)-5*cos(x)+6) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                          
  /                          
 |                           
 |          cos(x)           
 |  ---------------------- dx
 |     2                     
 |  cos (x) - 5*cos(x) + 6   
 |                           
/                            
0
∫01cos⁡(x)(cos⁡2(x)−5cos⁡(x))+6 dx\int\limits_{0}^{1} \frac{\cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} - 5 \cos{\left(x \right)}\right) + 6}\, dx 
Integral(cos(x)/(cos(x)^2 - 5*cos(x) + 6), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                           /        /x   pi\                     \           /        /x   pi\                     \
                                           |        |- - --|                     |           |        |- - --|                     |
  /                                    ___ |        |2   2 |       /  ___    /x\\|       ___ |        |2   2 |       /  ___    /x\\|
 |                                 3*\/ 2 *|pi*floor|------| + atan|\/ 2 *tan|-|||   4*\/ 3 *|pi*floor|------| + atan|\/ 3 *tan|-|||
 |         cos(x)                          \        \  pi  /       \         \2///           \        \  pi  /       \         \2///
 | ---------------------- dx = C - ----------------------------------------------- + -----------------------------------------------
 |    2                                                   2                                                 3                       
 | cos (x) - 5*cos(x) + 6                                                                                                           
 |                                                                                                                                  
/
∫cos⁡(x)(cos⁡2(x)−5cos⁡(x))+6 dx=C−32(atan⁡(2tan⁡(x2))+π⌊x2−π2π⌋)2+43(atan⁡(3tan⁡(x2))+π⌊x2−π2π⌋)3\int \frac{\cos{\left(x \right)}}{\left(\cos^{2}{\left(x \right)} - 5 \cos{\left(x \right)}\right) + 6}\, dx = C - \frac{3 \sqrt{2} \left(\operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{x}{2} \right)} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{2} + \frac{4 \sqrt{3} \left(\operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{x}{2} \right)} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901-1
Trazar el gráfico f(x)
Respuesta [src] 
         ___       ___ /          /  ___         \\          ___       ___ /          /  ___         \\
  3*pi*\/ 2    3*\/ 2 *\-pi + atan\\/ 2 *tan(1/2)//   4*pi*\/ 3    4*\/ 3 *\-pi + atan\\/ 3 *tan(1/2)//
- ---------- - ------------------------------------ + ---------- + ------------------------------------
      2                         2                         3                         3
−32π2+43(−π+atan⁡(3tan⁡(12)))3−32(−π+atan⁡(2tan⁡(12)))2+43π3- \frac{3 \sqrt{2} \pi}{2} + \frac{4 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{1}{2} \right)} \right)}\right)}{3} - \frac{3 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{1}{2} \right)} \right)}\right)}{2} + \frac{4 \sqrt{3} \pi}{3} 
=
= 
         ___       ___ /          /  ___         \\          ___       ___ /          /  ___         \\
  3*pi*\/ 2    3*\/ 2 *\-pi + atan\\/ 2 *tan(1/2)//   4*pi*\/ 3    4*\/ 3 *\-pi + atan\\/ 3 *tan(1/2)//
- ---------- - ------------------------------------ + ---------- + ------------------------------------
      2                         2                         3                         3
−32π2+43(−π+atan⁡(3tan⁡(12)))3−32(−π+atan⁡(2tan⁡(12)))2+43π3- \frac{3 \sqrt{2} \pi}{2} + \frac{4 \sqrt{3} \left(- \pi + \operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{1}{2} \right)} \right)}\right)}{3} - \frac{3 \sqrt{2} \left(- \pi + \operatorname{atan}{\left(\sqrt{2} \tan{\left(\frac{1}{2} \right)} \right)}\right)}{2} + \frac{4 \sqrt{3} \pi}{3} 
-3*pi*sqrt(2)/2 - 3*sqrt(2)*(-pi + atan(sqrt(2)*tan(1/2)))/2 + 4*pi*sqrt(3)/3 + 4*sqrt(3)*(-pi + atan(sqrt(3)*tan(1/2)))/3
Respuesta numérica [src] 
0.354596265816498
0.354596265816498

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

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