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Resolución de integrales/ 4cosx/ 1/(5+4cosx)^2

Integral de 1/(5+4cosx)^2 dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |                2   
 |  (5 + 4*cos(x))    
 |                    
/                     
0
∫011(4cos⁡(x)+5)2 dx\int\limits_{0}^{1} \frac{1}{\left(4 \cos{\left(x \right)} + 5\right)^{2}}\, dx 
Integral(1/((5 + 4*cos(x))^2), (x, 0, 1))
Respuesta (Indefinida) [src] 
                                                  /        /x   pi\       /   /x\\\              /        /x   pi\       /   /x\\\
                                                  |        |- - --|       |tan|-|||              |        |- - --|       |tan|-|||
  /                                  /x\          |        |2   2 |       |   \2/||         2/x\ |        |2   2 |       |   \2/||
 |                             24*tan|-|       90*|pi*floor|------| + atan|------||   10*tan |-|*|pi*floor|------| + atan|------||
 |        1                          \2/          \        \  pi  /       \  3   //          \2/ \        \  pi  /       \  3   //
 | --------------- dx = C - ---------------- + ------------------------------------ + --------------------------------------------
 |               2                      2/x\                         2/x\                                       2/x\              
 | (5 + 4*cos(x))           243 + 27*tan |-|             243 + 27*tan |-|                           243 + 27*tan |-|              
 |                                       \2/                          \2/                                        \2/              
/
∫1(4cos⁡(x)+5)2 dx=C+10(atan⁡(tan⁡(x2)3)+π⌊x2−π2π⌋)tan⁡2(x2)27tan⁡2(x2)+243+90(atan⁡(tan⁡(x2)3)+π⌊x2−π2π⌋)27tan⁡2(x2)+243−24tan⁡(x2)27tan⁡2(x2)+243\int \frac{1}{\left(4 \cos{\left(x \right)} + 5\right)^{2}}\, dx = C + \frac{10 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right) \tan^{2}{\left(\frac{x}{2} \right)}}{27 \tan^{2}{\left(\frac{x}{2} \right)} + 243} + \frac{90 \left(\operatorname{atan}{\left(\frac{\tan{\left(\frac{x}{2} \right)}}{3} \right)} + \pi \left\lfloor{\frac{\frac{x}{2} - \frac{\pi}{2}}{\pi}}\right\rfloor\right)}{27 \tan^{2}{\left(\frac{x}{2} \right)} + 243} - \frac{24 \tan{\left(\frac{x}{2} \right)}}{27 \tan^{2}{\left(\frac{x}{2} \right)} + 243}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901-2
Trazar el gráfico f(x)
Respuesta [src] 
                                /          /tan(1/2)\\         2      /          /tan(1/2)\\
                             90*|-pi + atan|--------||   10*tan (1/2)*|-pi + atan|--------||
10*pi      24*tan(1/2)          \          \   3    //                \          \   3    //
----- - ------------------ + ------------------------- + -----------------------------------
  27                2                        2                                2             
        243 + 27*tan (1/2)       243 + 27*tan (1/2)               243 + 27*tan (1/2)
90(−π+atan⁡(tan⁡(12)3))27tan⁡2(12)+243−24tan⁡(12)27tan⁡2(12)+243+10(−π+atan⁡(tan⁡(12)3))tan⁡2(12)27tan⁡2(12)+243+10π27\frac{90 \left(- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{27 \tan^{2}{\left(\frac{1}{2} \right)} + 243} - \frac{24 \tan{\left(\frac{1}{2} \right)}}{27 \tan^{2}{\left(\frac{1}{2} \right)} + 243} + \frac{10 \left(- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} \right)}\right) \tan^{2}{\left(\frac{1}{2} \right)}}{27 \tan^{2}{\left(\frac{1}{2} \right)} + 243} + \frac{10 \pi}{27} 
=
= 
                                /          /tan(1/2)\\         2      /          /tan(1/2)\\
                             90*|-pi + atan|--------||   10*tan (1/2)*|-pi + atan|--------||
10*pi      24*tan(1/2)          \          \   3    //                \          \   3    //
----- - ------------------ + ------------------------- + -----------------------------------
  27                2                        2                                2             
        243 + 27*tan (1/2)       243 + 27*tan (1/2)               243 + 27*tan (1/2)
90(−π+atan⁡(tan⁡(12)3))27tan⁡2(12)+243−24tan⁡(12)27tan⁡2(12)+243+10(−π+atan⁡(tan⁡(12)3))tan⁡2(12)27tan⁡2(12)+243+10π27\frac{90 \left(- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} \right)}\right)}{27 \tan^{2}{\left(\frac{1}{2} \right)} + 243} - \frac{24 \tan{\left(\frac{1}{2} \right)}}{27 \tan^{2}{\left(\frac{1}{2} \right)} + 243} + \frac{10 \left(- \pi + \operatorname{atan}{\left(\frac{\tan{\left(\frac{1}{2} \right)}}{3} \right)}\right) \tan^{2}{\left(\frac{1}{2} \right)}}{27 \tan^{2}{\left(\frac{1}{2} \right)} + 243} + \frac{10 \pi}{27} 
10*pi/27 - 24*tan(1/2)/(243 + 27*tan(1/2)^2) + 90*(-pi + atan(tan(1/2)/3))/(243 + 27*tan(1/2)^2) + 10*tan(1/2)^2*(-pi + atan(tan(1/2)/3))/(243 + 27*tan(1/2)^2)
Respuesta numérica [src] 
0.0144897209747261
0.0144897209747261

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

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