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Resolución de integrales/ (cosx)/ ((2-tgx)^10)/((cosx)^2)

Integral de ((2-tgx)^10)/((cosx)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 pi                  
 --                  
 4                   
  /                  
 |                   
 |              10   
 |  (2 - tan(x))     
 |  -------------- dx
 |        2          
 |     cos (x)       
 |                   
/                    
0
∫0π4(2−tan⁡(x))10cos⁡2(x) dx\int\limits_{0}^{\frac{\pi}{4}} \frac{\left(2 - \tan{\left(x \right)}\right)^{10}}{\cos^{2}{\left(x \right)}}\, dx 
Integral((2 - tan(x))^10/cos(x)^2, (x, 0, pi/4))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                  
 |                                                                                                                                                                                                                   
 |             10                                                      3                     4                   5                                                                                                   
 | (2 - tan(x))                    4        2560         /        2   \        /        2   \      /        2   \            2      6469*sin(x)   1931*sin(x)      sin(x)     215*sin(x)   4410*sin(x)   15038*sin(x)
 | -------------- dx = C - 3840*sec (x) - ------- - 1344*\-1 + sec (x)/  - 120*\-1 + sec (x)/  - 2*\-1 + sec (x)/  + 7680*sec (x) - ----------- - ----------- + ----------- + ---------- + ----------- + ------------
 |       2                                   2                                                                                       11*cos(x)           3            11            9             7             5    
 |    cos (x)                             cos (x)                                                                                                  11*cos (x)   11*cos  (x)   11*cos (x)    11*cos (x)    11*cos (x) 
 |                                                                                                                                                                                                                   
/
∫(2−tan⁡(x))10cos⁡2(x) dx=C−2(sec⁡2(x)−1)5−120(sec⁡2(x)−1)4−1344(sec⁡2(x)−1)3−6469sin⁡(x)11cos⁡(x)−1931sin⁡(x)11cos⁡3(x)+15038sin⁡(x)11cos⁡5(x)+4410sin⁡(x)11cos⁡7(x)+215sin⁡(x)11cos⁡9(x)+sin⁡(x)11cos⁡11(x)−3840sec⁡4(x)+7680sec⁡2(x)−2560cos⁡2(x)\int \frac{\left(2 - \tan{\left(x \right)}\right)^{10}}{\cos^{2}{\left(x \right)}}\, dx = C - 2 \left(\sec^{2}{\left(x \right)} - 1\right)^{5} - 120 \left(\sec^{2}{\left(x \right)} - 1\right)^{4} - 1344 \left(\sec^{2}{\left(x \right)} - 1\right)^{3} - \frac{6469 \sin{\left(x \right)}}{11 \cos{\left(x \right)}} - \frac{1931 \sin{\left(x \right)}}{11 \cos^{3}{\left(x \right)}} + \frac{15038 \sin{\left(x \right)}}{11 \cos^{5}{\left(x \right)}} + \frac{4410 \sin{\left(x \right)}}{11 \cos^{7}{\left(x \right)}} + \frac{215 \sin{\left(x \right)}}{11 \cos^{9}{\left(x \right)}} + \frac{\sin{\left(x \right)}}{11 \cos^{11}{\left(x \right)}} - 3840 \sec^{4}{\left(x \right)} + 7680 \sec^{2}{\left(x \right)} - \frac{2560}{\cos^{2}{\left(x \right)}}
Simplificar
Respuesta numérica [src] 
186.090909090909
186.090909090909

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

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