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Resolución de integrales/ sin^2/ cos^5/ sin^2x/cos^5x

Integral de sin^2x/cos^5x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1           
  /           
 |            
 |     2      
 |  sin (x)   
 |  ------- dx
 |     5      
 |  cos (x)   
 |            
/             
0
∫01sin⁡2(x)cos⁡5(x) dx\int\limits_{0}^{1} \frac{\sin^{2}{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx 
Integral(sin(x)^2/cos(x)^5, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                
 |                                                                                 
 |    2                                                          3                 
 | sin (x)          log(1 + sin(x))   log(-1 + sin(x))        sin (x) + sin(x)     
 | ------- dx = C - --------------- + ---------------- + --------------------------
 |    5                    16                16                    2           4   
 | cos (x)                                               8 - 16*sin (x) + 8*sin (x)
 |                                                                                 
/
∫sin⁡2(x)cos⁡5(x) dx=C+sin⁡3(x)+sin⁡(x)8sin⁡4(x)−16sin⁡2(x)+8+log⁡(sin⁡(x)−1)16−log⁡(sin⁡(x)+1)16\int \frac{\sin^{2}{\left(x \right)}}{\cos^{5}{\left(x \right)}}\, dx = C + \frac{\sin^{3}{\left(x \right)} + \sin{\left(x \right)}}{8 \sin^{4}{\left(x \right)} - 16 \sin^{2}{\left(x \right)} + 8} + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{16} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{16}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90020
Trazar el gráfico f(x)
Respuesta [src] 
                                              3                 
  log(1 + sin(1))   log(1 - sin(1))        sin (1) + sin(1)     
- --------------- + --------------- + --------------------------
         16                16                   2           4   
                                      8 - 16*sin (1) + 8*sin (1)
log⁡(1−sin⁡(1))16−log⁡(sin⁡(1)+1)16+sin⁡3(1)+sin⁡(1)−16sin⁡2(1)+8sin⁡4(1)+8\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} + \frac{\sin^{3}{\left(1 \right)} + \sin{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8} 
=
= 
                                              3                 
  log(1 + sin(1))   log(1 - sin(1))        sin (1) + sin(1)     
- --------------- + --------------- + --------------------------
         16                16                   2           4   
                                      8 - 16*sin (1) + 8*sin (1)
log⁡(1−sin⁡(1))16−log⁡(sin⁡(1)+1)16+sin⁡3(1)+sin⁡(1)−16sin⁡2(1)+8sin⁡4(1)+8\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{16} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{16} + \frac{\sin^{3}{\left(1 \right)} + \sin{\left(1 \right)}}{- 16 \sin^{2}{\left(1 \right)} + 8 \sin^{4}{\left(1 \right)} + 8} 
-log(1 + sin(1))/16 + log(1 - sin(1))/16 + (sin(1)^3 + sin(1))/(8 - 16*sin(1)^2 + 8*sin(1)^4)
Respuesta numérica [src] 
1.95490959678578
1.95490959678578

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

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