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Resolución de integrales/ cos^2/ sin^2/ 1/(2*cos^2(x)+sin^2(x)-5)

Integral de 1/(2*cos^2(x)+sin^2(x)-5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                           
  /                           
 |                            
 |             1              
 |  ----------------------- dx
 |       2         2          
 |  2*cos (x) + sin (x) - 5   
 |                            
/                             
0
∫011(sin⁡2(x)+2cos⁡2(x))−5 dx\int\limits_{0}^{1} \frac{1}{\left(\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right) - 5}\, dx 
Integral(1/(2*cos(x)^2 + sin(x)^2 - 5), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                          /        /x   pi\                     \         /        /x   pi\       /  ___    /x\\\
                                          |        |- - --|                     |         |        |- - --|       |\/ 3 *tan|-|||
  /                                   ___ |        |2   2 |       /  ___    /x\\|     ___ |        |2   2 |       |         \2/||
 |                                  \/ 3 *|pi*floor|------| + atan|\/ 3 *tan|-|||   \/ 3 *|pi*floor|------| + atan|------------||
 |            1                           \        \  pi  /       \         \2///         \        \  pi  /       \     3      //
 | ----------------------- dx = C - --------------------------------------------- - ---------------------------------------------
 |      2         2                                       6                                               6                      
 | 2*cos (x) + sin (x) - 5                                                                                                       
 |                                                                                                                               
/
∫1(sin⁡2(x)+2cos⁡2(x))−5 dx=C−3(atan⁡(3tan⁡(x2)3)+π⌊x2−π2π⌋)6−3(atan⁡(3tan⁡(x2))+π⌊x2−π2π⌋)6\int \frac{1}{\left(\sin^{2}{\left(x \right)} + 2 \cos^{2}{\left(x \right)}\right) - 5}\, dx = C - \frac{\sqrt{3} \left(\operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{x}{2} \right)}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{6} - \frac{\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)}{6}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902.5-2.5
Trazar el gráfico f(x)
Respuesta [src] 
                                                        /          /  ___         \\
                                                    ___ |          |\/ 3 *tan(1/2)||
       ___     ___ /          /  ___         \\   \/ 3 *|-pi + atan|--------------||
  pi*\/ 3    \/ 3 *\-pi + atan\\/ 3 *tan(1/2)//         \          \      3       //
- -------- - ---------------------------------- - ----------------------------------
     3                       6                                    6
−3π3−3(−π+atan⁡(3tan⁡(12)))6−3(−π+atan⁡(3tan⁡(12)3))6- \frac{\sqrt{3} \pi}{3} - \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{1}{2} \right)} \right)}\right)}{6} - \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{6} 
=
= 
                                                        /          /  ___         \\
                                                    ___ |          |\/ 3 *tan(1/2)||
       ___     ___ /          /  ___         \\   \/ 3 *|-pi + atan|--------------||
  pi*\/ 3    \/ 3 *\-pi + atan\\/ 3 *tan(1/2)//         \          \      3       //
- -------- - ---------------------------------- - ----------------------------------
     3                       6                                    6
−3π3−3(−π+atan⁡(3tan⁡(12)))6−3(−π+atan⁡(3tan⁡(12)3))6- \frac{\sqrt{3} \pi}{3} - \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\sqrt{3} \tan{\left(\frac{1}{2} \right)} \right)}\right)}{6} - \frac{\sqrt{3} \left(- \pi + \operatorname{atan}{\left(\frac{\sqrt{3} \tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{6} 
-pi*sqrt(3)/3 - sqrt(3)*(-pi + atan(sqrt(3)*tan(1/2)))/6 - sqrt(3)*(-pi + atan(sqrt(3)*tan(1/2)/3))/6
Respuesta numérica [src] 
-0.306949981825035
-0.306949981825035

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

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