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Resolución de integrales/ (x)^2/ cos(x)/ sin(x)/ x/(sin(x)^2*cos(x)^2)

Integral de x/(sin(x)^2*cos(x)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         x          
 |  --------------- dx
 |     2       2      
 |  sin (x)*cos (x)   
 |                    
/                     
0
∫01xsin⁡2(x)cos⁡2(x) dx\int\limits_{0}^{1} \frac{x}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\, dx 
Integral(x/((sin(x)^2*cos(x)^2)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                             4/x\                      2/x\              3/x\    /       2/x\\        /       /x\\    /x\        /        /x\\    /x\         /   /x\\    /x\         3/x\    /       /x\\        3/x\    /        /x\\        3/x\    /   /x\\         /       2/x\\    /x\
 |                                                         x*tan |-|               6*x*tan |-|         4*tan |-|*log|1 + tan |-||   2*log|1 + tan|-||*tan|-|   2*log|-1 + tan|-||*tan|-|    2*log|tan|-||*tan|-|    2*tan |-|*log|1 + tan|-||   2*tan |-|*log|-1 + tan|-||   2*tan |-|*log|tan|-||    4*log|1 + tan |-||*tan|-|
 |        x                           x                          \2/                       \2/               \2/    \        \2//        \       \2//    \2/        \        \2//    \2/         \   \2//    \2/          \2/    \       \2//         \2/    \        \2//         \2/    \   \2//         \        \2//    \2/
 | --------------- dx = C + ---------------------- + ---------------------- - ---------------------- - -------------------------- - ------------------------ - ------------------------- - ---------------------- + ------------------------- + -------------------------- + ---------------------- + -------------------------
 |    2       2                    /x\        3/x\          /x\        3/x\          /x\        3/x\            /x\        3/x\             /x\        3/x\             /x\        3/x\           /x\        3/x\            /x\        3/x\             /x\        3/x\            /x\        3/x\            /x\        3/x\ 
 | sin (x)*cos (x)          - 2*tan|-| + 2*tan |-|   - 2*tan|-| + 2*tan |-|   - 2*tan|-| + 2*tan |-|     - 2*tan|-| + 2*tan |-|      - 2*tan|-| + 2*tan |-|      - 2*tan|-| + 2*tan |-|    - 2*tan|-| + 2*tan |-|     - 2*tan|-| + 2*tan |-|      - 2*tan|-| + 2*tan |-|     - 2*tan|-| + 2*tan |-|     - 2*tan|-| + 2*tan |-| 
 |                                 \2/         \2/          \2/         \2/          \2/         \2/            \2/         \2/             \2/         \2/             \2/         \2/           \2/         \2/            \2/         \2/             \2/         \2/            \2/         \2/            \2/         \2/ 
/
∫xsin⁡2(x)cos⁡2(x) dx=C+xtan⁡4(x2)2tan⁡3(x2)−2tan⁡(x2)−6xtan⁡2(x2)2tan⁡3(x2)−2tan⁡(x2)+x2tan⁡3(x2)−2tan⁡(x2)+2log⁡(tan⁡(x2)−1)tan⁡3(x2)2tan⁡3(x2)−2tan⁡(x2)−2log⁡(tan⁡(x2)−1)tan⁡(x2)2tan⁡3(x2)−2tan⁡(x2)+2log⁡(tan⁡(x2)+1)tan⁡3(x2)2tan⁡3(x2)−2tan⁡(x2)−2log⁡(tan⁡(x2)+1)tan⁡(x2)2tan⁡3(x2)−2tan⁡(x2)−4log⁡(tan⁡2(x2)+1)tan⁡3(x2)2tan⁡3(x2)−2tan⁡(x2)+4log⁡(tan⁡2(x2)+1)tan⁡(x2)2tan⁡3(x2)−2tan⁡(x2)+2log⁡(tan⁡(x2))tan⁡3(x2)2tan⁡3(x2)−2tan⁡(x2)−2log⁡(tan⁡(x2))tan⁡(x2)2tan⁡3(x2)−2tan⁡(x2)\int \frac{x}{\sin^{2}{\left(x \right)} \cos^{2}{\left(x \right)}}\, dx = C + \frac{x \tan^{4}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} - \frac{6 x \tan^{2}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} + \frac{x}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} - 1 \right)} \tan{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} + 1 \right)} \tan{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} - \frac{4 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} + \frac{4 \log{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1 \right)} \tan{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} + \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan^{3}{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}} - \frac{2 \log{\left(\tan{\left(\frac{x}{2} \right)} \right)} \tan{\left(\frac{x}{2} \right)}}{2 \tan^{3}{\left(\frac{x}{2} \right)} - 2 \tan{\left(\frac{x}{2} \right)}}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90020000
Trazar el gráfico f(x)
Respuesta [src] 
                                                  3                                
     2*(pi*I + log(1 - tan(1/2)))*tan(1/2)   2*tan (1/2)*(pi*I + log(1 - tan(1/2)))
oo - ------------------------------------- + --------------------------------------
                              3                                       3            
           -2*tan(1/2) + 2*tan (1/2)               -2*tan(1/2) + 2*tan (1/2)
∞+2(log⁡(1−tan⁡(12))+iπ)tan⁡3(12)−2tan⁡(12)+2tan⁡3(12)−2(log⁡(1−tan⁡(12))+iπ)tan⁡(12)−2tan⁡(12)+2tan⁡3(12)\infty + \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{3}{\left(\frac{1}{2} \right)}}{- 2 \tan{\left(\frac{1}{2} \right)} + 2 \tan^{3}{\left(\frac{1}{2} \right)}} - \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan{\left(\frac{1}{2} \right)}}{- 2 \tan{\left(\frac{1}{2} \right)} + 2 \tan^{3}{\left(\frac{1}{2} \right)}} 
=
= 
                                                  3                                
     2*(pi*I + log(1 - tan(1/2)))*tan(1/2)   2*tan (1/2)*(pi*I + log(1 - tan(1/2)))
oo - ------------------------------------- + --------------------------------------
                              3                                       3            
           -2*tan(1/2) + 2*tan (1/2)               -2*tan(1/2) + 2*tan (1/2)
∞+2(log⁡(1−tan⁡(12))+iπ)tan⁡3(12)−2tan⁡(12)+2tan⁡3(12)−2(log⁡(1−tan⁡(12))+iπ)tan⁡(12)−2tan⁡(12)+2tan⁡3(12)\infty + \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan^{3}{\left(\frac{1}{2} \right)}}{- 2 \tan{\left(\frac{1}{2} \right)} + 2 \tan^{3}{\left(\frac{1}{2} \right)}} - \frac{2 \left(\log{\left(1 - \tan{\left(\frac{1}{2} \right)} \right)} + i \pi\right) \tan{\left(\frac{1}{2} \right)}}{- 2 \tan{\left(\frac{1}{2} \right)} + 2 \tan^{3}{\left(\frac{1}{2} \right)}} 
oo - 2*(pi*i + log(1 - tan(1/2)))*tan(1/2)/(-2*tan(1/2) + 2*tan(1/2)^3) + 2*tan(1/2)^3*(pi*i + log(1 - tan(1/2)))/(-2*tan(1/2) + 2*tan(1/2)^3)
Respuesta numérica [src] 
45.2175310260584
45.2175310260584

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

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