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Resolución de integrales/ 1/sin/ sin^2/ 1/sin^23x

Integral de 1/sin^23x dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     1       
 |  -------- dx
 |     23      
 |  sin  (x)   
 |             
/              
0
∫011sin⁡23(x) dx\int\limits_{0}^{1} \frac{1}{\sin^{23}{\left(x \right)}}\, dx 
Integral(1/(sin(x)^23), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                                            
 |                                                                                               11                    7                    15                   3                   19                  21                                     17                    5                    13                    9             
 |    1              88179*log(1 + cos(x))   88179*log(-1 + cos(x))              - 5503713280*cos  (x) - 3424523520*cos (x) - 2163862272*cos  (x) - 450357600*cos (x) - 155195040*cos  (x) + 14549535*cos  (x) + 71957985*cos(x) + 749786037*cos  (x) + 1551313995*cos (x) + 4139920070*cos  (x) + 5174056250*cos (x)          
 | -------- dx = C - --------------------- + ---------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |    23                    1048576                 1048576                                      12                     8                     16                    4                   20                  22                   2                    18                     6                     14                     10   
 | sin  (x)                                                           -86507520 - 39966474240*cos  (x) - 28547481600*cos (x) - 14273740800*cos  (x) - 4757913600*cos (x) - 951582720*cos  (x) + 86507520*cos  (x) + 951582720*cos (x) + 4757913600*cos  (x) + 14273740800*cos (x) + 28547481600*cos  (x) + 39966474240*cos  (x)
 |                                                                                                                                                                                                                                                                                                                             
/
∫1sin⁡23(x) dx=C+14549535cos⁡21(x)−155195040cos⁡19(x)+749786037cos⁡17(x)−2163862272cos⁡15(x)+4139920070cos⁡13(x)−5503713280cos⁡11(x)+5174056250cos⁡9(x)−3424523520cos⁡7(x)+1551313995cos⁡5(x)−450357600cos⁡3(x)+71957985cos⁡(x)86507520cos⁡22(x)−951582720cos⁡20(x)+4757913600cos⁡18(x)−14273740800cos⁡16(x)+28547481600cos⁡14(x)−39966474240cos⁡12(x)+39966474240cos⁡10(x)−28547481600cos⁡8(x)+14273740800cos⁡6(x)−4757913600cos⁡4(x)+951582720cos⁡2(x)−86507520+88179log⁡(cos⁡(x)−1)1048576−88179log⁡(cos⁡(x)+1)1048576\int \frac{1}{\sin^{23}{\left(x \right)}}\, dx = C + \frac{14549535 \cos^{21}{\left(x \right)} - 155195040 \cos^{19}{\left(x \right)} + 749786037 \cos^{17}{\left(x \right)} - 2163862272 \cos^{15}{\left(x \right)} + 4139920070 \cos^{13}{\left(x \right)} - 5503713280 \cos^{11}{\left(x \right)} + 5174056250 \cos^{9}{\left(x \right)} - 3424523520 \cos^{7}{\left(x \right)} + 1551313995 \cos^{5}{\left(x \right)} - 450357600 \cos^{3}{\left(x \right)} + 71957985 \cos{\left(x \right)}}{86507520 \cos^{22}{\left(x \right)} - 951582720 \cos^{20}{\left(x \right)} + 4757913600 \cos^{18}{\left(x \right)} - 14273740800 \cos^{16}{\left(x \right)} + 28547481600 \cos^{14}{\left(x \right)} - 39966474240 \cos^{12}{\left(x \right)} + 39966474240 \cos^{10}{\left(x \right)} - 28547481600 \cos^{8}{\left(x \right)} + 14273740800 \cos^{6}{\left(x \right)} - 4757913600 \cos^{4}{\left(x \right)} + 951582720 \cos^{2}{\left(x \right)} - 86507520} + \frac{88179 \log{\left(\cos{\left(x \right)} - 1 \right)}}{1048576} - \frac{88179 \log{\left(\cos{\left(x \right)} + 1 \right)}}{1048576}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.90-1e921e92
Trazar el gráfico f(x)
Respuesta numérica [src] 
6.53781434193313e+417
6.53781434193313e+417

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

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