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Resolución de integrales/ sin^3/ x×cosx/ 1/(sin^33x×cosx)

Integral de 1/(sin^33x×cosx) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                   
  /                   
 |                    
 |         1          
 |  --------------- dx
 |     33             
 |  sin  (x)*cos(x)   
 |                    
/                     
0
∫011sin⁡33(x)cos⁡(x) dx\int\limits_{0}^{1} \frac{1}{\sin^{33}{\left(x \right)} \cos{\left(x \right)}}\, dx 
Integral(1/(sin(x)^33*cos(x)), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                                                  
 |                             /        2   \                    2               4               6               8               10               12               14               16                18                20                22                24                26                28                30                 
 |        1                 log\-1 + sin (x)/   45045 + 48048*sin (x) + 51480*sin (x) + 55440*sin (x) + 60060*sin (x) + 65520*sin  (x) + 72072*sin  (x) + 80080*sin  (x) + 90090*sin  (x) + 102960*sin  (x) + 120120*sin  (x) + 144144*sin  (x) + 180180*sin  (x) + 240240*sin  (x) + 360360*sin  (x) + 720720*sin  (x)              
 | --------------- dx = C - ----------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + log(sin(x))
 |    33                            2                                                                                                                                                  32                                                                                                                                            
 | sin  (x)*cos(x)                                                                                                                                                          1441440*sin  (x)                                                                                                                                         
 |                                                                                                                                                                                                                                                                                                                                   
/
∫1sin⁡33(x)cos⁡(x) dx=C−720720sin⁡30(x)+360360sin⁡28(x)+240240sin⁡26(x)+180180sin⁡24(x)+144144sin⁡22(x)+120120sin⁡20(x)+102960sin⁡18(x)+90090sin⁡16(x)+80080sin⁡14(x)+72072sin⁡12(x)+65520sin⁡10(x)+60060sin⁡8(x)+55440sin⁡6(x)+51480sin⁡4(x)+48048sin⁡2(x)+450451441440sin⁡32(x)−log⁡(sin⁡2(x)−1)2+log⁡(sin⁡(x))\int \frac{1}{\sin^{33}{\left(x \right)} \cos{\left(x \right)}}\, dx = C - \frac{720720 \sin^{30}{\left(x \right)} + 360360 \sin^{28}{\left(x \right)} + 240240 \sin^{26}{\left(x \right)} + 180180 \sin^{24}{\left(x \right)} + 144144 \sin^{22}{\left(x \right)} + 120120 \sin^{20}{\left(x \right)} + 102960 \sin^{18}{\left(x \right)} + 90090 \sin^{16}{\left(x \right)} + 80080 \sin^{14}{\left(x \right)} + 72072 \sin^{12}{\left(x \right)} + 65520 \sin^{10}{\left(x \right)} + 60060 \sin^{8}{\left(x \right)} + 55440 \sin^{6}{\left(x \right)} + 51480 \sin^{4}{\left(x \right)} + 48048 \sin^{2}{\left(x \right)} + 45045}{1441440 \sin^{32}{\left(x \right)}} - \frac{\log{\left(\sin^{2}{\left(x \right)} - 1 \right)}}{2} + \log{\left(\sin{\left(x \right)} \right)}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.901e131-5e130
Trazar el gráfico f(x)
Respuesta [src] 
     pi*I
oo - ----
      2
∞−iπ2\infty - \frac{i \pi}{2} 
=
= 
     pi*I
oo - ----
      2
∞−iπ2\infty - \frac{i \pi}{2} 
oo - pi*i/2
Respuesta numérica [src] 
6.3991619231389e+607
6.3991619231389e+607

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

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