Sr Examen

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Resolución de integrales/ (24*sin(x)^5)/((cos(x)+1)^5)-((20*sin(x)^3)/((cos(x)+1)^3))+(sin(x))/(cos(x)+1)-(15*cos(x)*sin(x))/((cos(x)+1)^2)

Integral de (24*sin(x)^5)/((cos(x)+1)^5)-((20*sin(x)^3)/((cos(x)+1)^3))+(sin(x))/(cos(x)+1)-(15*cos(x)*sin(x))/((cos(x)+1)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                                                                   
  /                                                                   
 |                                                                    
 |  /        5               3                                    \   
 |  |  24*sin (x)      20*sin (x)      sin(x)     15*cos(x)*sin(x)|   
 |  |------------- - ------------- + ---------- - ----------------| dx
 |  |            5               3   cos(x) + 1                2  |   
 |  \(cos(x) + 1)    (cos(x) + 1)                  (cos(x) + 1)   /   
 |                                                                    
/                                                                     
0
∫01(−sin⁡(x)15cos⁡(x)(cos⁡(x)+1)2+((24sin⁡5(x)(cos⁡(x)+1)5−20sin⁡3(x)(cos⁡(x)+1)3)+sin⁡(x)cos⁡(x)+1)) dx\int\limits_{0}^{1} \left(- \frac{\sin{\left(x \right)} 15 \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{2}} + \left(\left(\frac{24 \sin^{5}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{5}} - \frac{20 \sin^{3}{\left(x \right)}}{\left(\cos{\left(x \right)} + 1\right)^{3}}\right) + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)} + 1}\right)\right)\, dx 
Integral((24*sin(x)^5)/(cos(x) + 1)^5 - 20*sin(x)^3/(cos(x) + 1)^3 + sin(x)/(cos(x) + 1) - (15*cos(x))*sin(x)/(cos(x) + 1)^2, (x, 0, 1))
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-5050
Trazar el gráfico f(x)
Respuesta [src] 
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41                                              384                                       40                  15                                        1344*cos (1)                                            1248*cos(1)                                             480*cos (1)                                         288*log(1 + cos(1))                                          48*sin (1)                               40*cos(1)              40*log(1 + cos(1))             20*sin (1)          15*log(1 + cos(1))                         72*sin (1)                                     1728*cos (1)*log(1 + cos(1))                            1152*cos (1)*log(1 + cos(1))                            1152*cos(1)*log(1 + cos(1))                             288*cos (1)*log(1 + cos(1))                                  192*sin (1)*cos(1)                                     144*cos (1)*sin (1)                    80*cos(1)*log(1 + cos(1))   40*cos (1)*log(1 + cos(1))   15*cos(1)*log(1 + cos(1))
-- - log(1 + cos(1)) - ----------------------------------------------------- - ------------------------ + ---------- + 30*log(2) - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ------------------------ - ------------------------ - ------------------------ + ------------------ + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ------------------------- - -------------------------- + -------------------------
2                                 4            3                        2               2                 1 + cos(1)                          4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2               2                          2                          2                     1 + cos(1)                  4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                2                           2                          1 + cos(1)       
                       12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   2 + 2*cos (1) + 4*cos(1)                            12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   2 + 2*cos (1) + 4*cos(1)   2 + 2*cos (1) + 4*cos(1)   2 + 2*cos (1) + 4*cos(1)                        12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)    2 + 2*cos (1) + 4*cos(1)    2 + 2*cos (1) + 4*cos(1)
−1248cos⁡(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−402cos⁡2(1)+2+4cos⁡(1)−1344cos⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−38412cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−40cos⁡(1)2cos⁡2(1)+2+4cos⁡(1)−1152log⁡(cos⁡(1)+1)cos⁡(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−80log⁡(cos⁡(1)+1)cos⁡(1)2cos⁡2(1)+2+4cos⁡(1)−40log⁡(cos⁡(1)+1)2cos⁡2(1)+2+4cos⁡(1)−1728log⁡(cos⁡(1)+1)cos⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−20sin⁡2(1)2cos⁡2(1)+2+4cos⁡(1)−288log⁡(cos⁡(1)+1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−1152log⁡(cos⁡(1)+1)cos⁡3(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−480cos⁡3(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−192sin⁡2(1)cos⁡(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−40log⁡(cos⁡(1)+1)cos⁡2(1)2cos⁡2(1)+2+4cos⁡(1)−48sin⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−144sin⁡2(1)cos⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−log⁡(cos⁡(1)+1)−288log⁡(cos⁡(1)+1)cos⁡4(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)+72sin⁡4(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)+15log⁡(cos⁡(1)+1)cos⁡(1)cos⁡(1)+1+15log⁡(cos⁡(1)+1)cos⁡(1)+1+15cos⁡(1)+1+412+30log⁡(2)- \frac{1248 \cos{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{40}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{1344 \cos^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{384}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{40 \cos{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{1152 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{80 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{40 \log{\left(\cos{\left(1 \right)} + 1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{1728 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{20 \sin^{2}{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{288 \log{\left(\cos{\left(1 \right)} + 1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{1152 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{3}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{480 \cos^{3}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{192 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{40 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{2}{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{48 \sin^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{144 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \log{\left(\cos{\left(1 \right)} + 1 \right)} - \frac{288 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{4}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} + \frac{72 \sin^{4}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} + \frac{15 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos{\left(1 \right)}}{\cos{\left(1 \right)} + 1} + \frac{15 \log{\left(\cos{\left(1 \right)} + 1 \right)}}{\cos{\left(1 \right)} + 1} + \frac{15}{\cos{\left(1 \right)} + 1} + \frac{41}{2} + 30 \log{\left(2 \right)} 
=
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41                                              384                                       40                  15                                        1344*cos (1)                                            1248*cos(1)                                             480*cos (1)                                         288*log(1 + cos(1))                                          48*sin (1)                               40*cos(1)              40*log(1 + cos(1))             20*sin (1)          15*log(1 + cos(1))                         72*sin (1)                                     1728*cos (1)*log(1 + cos(1))                            1152*cos (1)*log(1 + cos(1))                            1152*cos(1)*log(1 + cos(1))                             288*cos (1)*log(1 + cos(1))                                  192*sin (1)*cos(1)                                     144*cos (1)*sin (1)                    80*cos(1)*log(1 + cos(1))   40*cos (1)*log(1 + cos(1))   15*cos(1)*log(1 + cos(1))
-- - log(1 + cos(1)) - ----------------------------------------------------- - ------------------------ + ---------- + 30*log(2) - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ------------------------ - ------------------------ - ------------------------ + ------------------ + ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ----------------------------------------------------- - ------------------------- - -------------------------- + -------------------------
2                                 4            3                        2               2                 1 + cos(1)                          4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2               2                          2                          2                     1 + cos(1)                  4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                 4            3                        2                2                           2                          1 + cos(1)       
                       12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   2 + 2*cos (1) + 4*cos(1)                            12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   2 + 2*cos (1) + 4*cos(1)   2 + 2*cos (1) + 4*cos(1)   2 + 2*cos (1) + 4*cos(1)                        12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)   12 + 12*cos (1) + 48*cos (1) + 48*cos(1) + 72*cos (1)    2 + 2*cos (1) + 4*cos(1)    2 + 2*cos (1) + 4*cos(1)
−1248cos⁡(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−402cos⁡2(1)+2+4cos⁡(1)−1344cos⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−38412cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−40cos⁡(1)2cos⁡2(1)+2+4cos⁡(1)−1152log⁡(cos⁡(1)+1)cos⁡(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−80log⁡(cos⁡(1)+1)cos⁡(1)2cos⁡2(1)+2+4cos⁡(1)−40log⁡(cos⁡(1)+1)2cos⁡2(1)+2+4cos⁡(1)−1728log⁡(cos⁡(1)+1)cos⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−20sin⁡2(1)2cos⁡2(1)+2+4cos⁡(1)−288log⁡(cos⁡(1)+1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−1152log⁡(cos⁡(1)+1)cos⁡3(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−480cos⁡3(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−192sin⁡2(1)cos⁡(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−40log⁡(cos⁡(1)+1)cos⁡2(1)2cos⁡2(1)+2+4cos⁡(1)−48sin⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−144sin⁡2(1)cos⁡2(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)−log⁡(cos⁡(1)+1)−288log⁡(cos⁡(1)+1)cos⁡4(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)+72sin⁡4(1)12cos⁡4(1)+48cos⁡3(1)+12+72cos⁡2(1)+48cos⁡(1)+15log⁡(cos⁡(1)+1)cos⁡(1)cos⁡(1)+1+15log⁡(cos⁡(1)+1)cos⁡(1)+1+15cos⁡(1)+1+412+30log⁡(2)- \frac{1248 \cos{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{40}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{1344 \cos^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{384}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{40 \cos{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{1152 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{80 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{40 \log{\left(\cos{\left(1 \right)} + 1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{1728 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{20 \sin^{2}{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{288 \log{\left(\cos{\left(1 \right)} + 1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{1152 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{3}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{480 \cos^{3}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{192 \sin^{2}{\left(1 \right)} \cos{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{40 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{2}{\left(1 \right)}}{2 \cos^{2}{\left(1 \right)} + 2 + 4 \cos{\left(1 \right)}} - \frac{48 \sin^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \frac{144 \sin^{2}{\left(1 \right)} \cos^{2}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} - \log{\left(\cos{\left(1 \right)} + 1 \right)} - \frac{288 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos^{4}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} + \frac{72 \sin^{4}{\left(1 \right)}}{12 \cos^{4}{\left(1 \right)} + 48 \cos^{3}{\left(1 \right)} + 12 + 72 \cos^{2}{\left(1 \right)} + 48 \cos{\left(1 \right)}} + \frac{15 \log{\left(\cos{\left(1 \right)} + 1 \right)} \cos{\left(1 \right)}}{\cos{\left(1 \right)} + 1} + \frac{15 \log{\left(\cos{\left(1 \right)} + 1 \right)}}{\cos{\left(1 \right)} + 1} + \frac{15}{\cos{\left(1 \right)} + 1} + \frac{41}{2} + 30 \log{\left(2 \right)} 
41/2 - log(1 + cos(1)) - 384/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 40/(2 + 2*cos(1)^2 + 4*cos(1)) + 15/(1 + cos(1)) + 30*log(2) - 1344*cos(1)^2/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 1248*cos(1)/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 480*cos(1)^3/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 288*log(1 + cos(1))/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 48*sin(1)^2/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 40*cos(1)/(2 + 2*cos(1)^2 + 4*cos(1)) - 40*log(1 + cos(1))/(2 + 2*cos(1)^2 + 4*cos(1)) - 20*sin(1)^2/(2 + 2*cos(1)^2 + 4*cos(1)) + 15*log(1 + cos(1))/(1 + cos(1)) + 72*sin(1)^4/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 1728*cos(1)^2*log(1 + cos(1))/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 1152*cos(1)^3*log(1 + cos(1))/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 1152*cos(1)*log(1 + cos(1))/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 288*cos(1)^4*log(1 + cos(1))/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 192*sin(1)^2*cos(1)/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 144*cos(1)^2*sin(1)^2/(12 + 12*cos(1)^4 + 48*cos(1)^3 + 48*cos(1) + 72*cos(1)^2) - 80*cos(1)*log(1 + cos(1))/(2 + 2*cos(1)^2 + 4*cos(1)) - 40*cos(1)^2*log(1 + cos(1))/(2 + 2*cos(1)^2 + 4*cos(1)) + 15*cos(1)*log(1 + cos(1))/(1 + cos(1))
Respuesta numérica [src] 
-1.98939643468833
-1.98939643468833

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

    © Sr Examen – Калькулятор