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Resolución de integrales/ cos²3x/ 1/(cos²3x)

Integral de 1/(cos²3x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |     1       
 |  -------- dx
 |     23      
 |  cos  (x)   
 |             
/              
0
∫011cos⁡23(x) dx\int\limits_{0}^{1} \frac{1}{\cos^{23}{\left(x \right)}}\, dx 
Integral(1/(cos(x)^23), (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                                                                                                            
 |                                                                                               11                    7                    15                   3                   19                  21                                     17                    5                    13                    9             
 |    1              88179*log(-1 + sin(x))   88179*log(1 + sin(x))              - 5503713280*sin  (x) - 3424523520*sin (x) - 2163862272*sin  (x) - 450357600*sin (x) - 155195040*sin  (x) + 14549535*sin  (x) + 71957985*sin(x) + 749786037*sin  (x) + 1551313995*sin (x) + 4139920070*sin  (x) + 5174056250*sin (x)          
 | -------- dx = C - ---------------------- + --------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
 |    23                    1048576                  1048576                                     12                     8                     16                    4                   20                  22                   2                    18                     6                     14                     10   
 | cos  (x)                                                           -86507520 - 39966474240*sin  (x) - 28547481600*sin (x) - 14273740800*sin  (x) - 4757913600*sin (x) - 951582720*sin  (x) + 86507520*sin  (x) + 951582720*sin (x) + 4757913600*sin  (x) + 14273740800*sin (x) + 28547481600*sin  (x) + 39966474240*sin  (x)
 |                                                                                                                                                                                                                                                                                                                             
/
∫1cos⁡23(x) dx=C−14549535sin⁡21(x)−155195040sin⁡19(x)+749786037sin⁡17(x)−2163862272sin⁡15(x)+4139920070sin⁡13(x)−5503713280sin⁡11(x)+5174056250sin⁡9(x)−3424523520sin⁡7(x)+1551313995sin⁡5(x)−450357600sin⁡3(x)+71957985sin⁡(x)86507520sin⁡22(x)−951582720sin⁡20(x)+4757913600sin⁡18(x)−14273740800sin⁡16(x)+28547481600sin⁡14(x)−39966474240sin⁡12(x)+39966474240sin⁡10(x)−28547481600sin⁡8(x)+14273740800sin⁡6(x)−4757913600sin⁡4(x)+951582720sin⁡2(x)−86507520−88179log⁡(sin⁡(x)−1)1048576+88179log⁡(sin⁡(x)+1)1048576\int \frac{1}{\cos^{23}{\left(x \right)}}\, dx = C - \frac{14549535 \sin^{21}{\left(x \right)} - 155195040 \sin^{19}{\left(x \right)} + 749786037 \sin^{17}{\left(x \right)} - 2163862272 \sin^{15}{\left(x \right)} + 4139920070 \sin^{13}{\left(x \right)} - 5503713280 \sin^{11}{\left(x \right)} + 5174056250 \sin^{9}{\left(x \right)} - 3424523520 \sin^{7}{\left(x \right)} + 1551313995 \sin^{5}{\left(x \right)} - 450357600 \sin^{3}{\left(x \right)} + 71957985 \sin{\left(x \right)}}{86507520 \sin^{22}{\left(x \right)} - 951582720 \sin^{20}{\left(x \right)} + 4757913600 \sin^{18}{\left(x \right)} - 14273740800 \sin^{16}{\left(x \right)} + 28547481600 \sin^{14}{\left(x \right)} - 39966474240 \sin^{12}{\left(x \right)} + 39966474240 \sin^{10}{\left(x \right)} - 28547481600 \sin^{8}{\left(x \right)} + 14273740800 \sin^{6}{\left(x \right)} - 4757913600 \sin^{4}{\left(x \right)} + 951582720 \sin^{2}{\left(x \right)} - 86507520} - \frac{88179 \log{\left(\sin{\left(x \right)} - 1 \right)}}{1048576} + \frac{88179 \log{\left(\sin{\left(x \right)} + 1 \right)}}{1048576}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002000000
Trazar el gráfico f(x)
Respuesta [src] 
                                                                             11                    7                    15                   3                   19                  21                                     17                    5                    13                    9             
  88179*log(1 - sin(1))   88179*log(1 + sin(1))              - 5503713280*sin  (1) - 3424523520*sin (1) - 2163862272*sin  (1) - 450357600*sin (1) - 155195040*sin  (1) + 14549535*sin  (1) + 71957985*sin(1) + 749786037*sin  (1) + 1551313995*sin (1) + 4139920070*sin  (1) + 5174056250*sin (1)          
- --------------------- + --------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
         1048576                 1048576                                     12                     8                     16                    4                   20                  22                   2                    18                     6                     14                     10   
                                                  -86507520 - 39966474240*sin  (1) - 28547481600*sin (1) - 14273740800*sin  (1) - 4757913600*sin (1) - 951582720*sin  (1) + 86507520*sin  (1) + 951582720*sin (1) + 4757913600*sin  (1) + 14273740800*sin (1) + 28547481600*sin  (1) + 39966474240*sin  (1)
88179log⁡(sin⁡(1)+1)1048576−88179log⁡(1−sin⁡(1))1048576−−3424523520sin⁡7(1)−5503713280sin⁡11(1)−450357600sin⁡3(1)−2163862272sin⁡15(1)−155195040sin⁡19(1)+14549535sin⁡21(1)+749786037sin⁡17(1)+71957985sin⁡(1)+4139920070sin⁡13(1)+1551313995sin⁡5(1)+5174056250sin⁡9(1)−28547481600sin⁡8(1)−39966474240sin⁡12(1)−4757913600sin⁡4(1)−14273740800sin⁡16(1)−86507520−951582720sin⁡20(1)+86507520sin⁡22(1)+4757913600sin⁡18(1)+951582720sin⁡2(1)+28547481600sin⁡14(1)+14273740800sin⁡6(1)+39966474240sin⁡10(1)\frac{88179 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{1048576} - \frac{88179 \log{\left(1 - \sin{\left(1 \right)} \right)}}{1048576} - \frac{- 3424523520 \sin^{7}{\left(1 \right)} - 5503713280 \sin^{11}{\left(1 \right)} - 450357600 \sin^{3}{\left(1 \right)} - 2163862272 \sin^{15}{\left(1 \right)} - 155195040 \sin^{19}{\left(1 \right)} + 14549535 \sin^{21}{\left(1 \right)} + 749786037 \sin^{17}{\left(1 \right)} + 71957985 \sin{\left(1 \right)} + 4139920070 \sin^{13}{\left(1 \right)} + 1551313995 \sin^{5}{\left(1 \right)} + 5174056250 \sin^{9}{\left(1 \right)}}{- 28547481600 \sin^{8}{\left(1 \right)} - 39966474240 \sin^{12}{\left(1 \right)} - 4757913600 \sin^{4}{\left(1 \right)} - 14273740800 \sin^{16}{\left(1 \right)} - 86507520 - 951582720 \sin^{20}{\left(1 \right)} + 86507520 \sin^{22}{\left(1 \right)} + 4757913600 \sin^{18}{\left(1 \right)} + 951582720 \sin^{2}{\left(1 \right)} + 28547481600 \sin^{14}{\left(1 \right)} + 14273740800 \sin^{6}{\left(1 \right)} + 39966474240 \sin^{10}{\left(1 \right)}} 
=
= 
                                                                             11                    7                    15                   3                   19                  21                                     17                    5                    13                    9             
  88179*log(1 - sin(1))   88179*log(1 + sin(1))              - 5503713280*sin  (1) - 3424523520*sin (1) - 2163862272*sin  (1) - 450357600*sin (1) - 155195040*sin  (1) + 14549535*sin  (1) + 71957985*sin(1) + 749786037*sin  (1) + 1551313995*sin (1) + 4139920070*sin  (1) + 5174056250*sin (1)          
- --------------------- + --------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
         1048576                 1048576                                     12                     8                     16                    4                   20                  22                   2                    18                     6                     14                     10   
                                                  -86507520 - 39966474240*sin  (1) - 28547481600*sin (1) - 14273740800*sin  (1) - 4757913600*sin (1) - 951582720*sin  (1) + 86507520*sin  (1) + 951582720*sin (1) + 4757913600*sin  (1) + 14273740800*sin (1) + 28547481600*sin  (1) + 39966474240*sin  (1)
88179log⁡(sin⁡(1)+1)1048576−88179log⁡(1−sin⁡(1))1048576−−3424523520sin⁡7(1)−5503713280sin⁡11(1)−450357600sin⁡3(1)−2163862272sin⁡15(1)−155195040sin⁡19(1)+14549535sin⁡21(1)+749786037sin⁡17(1)+71957985sin⁡(1)+4139920070sin⁡13(1)+1551313995sin⁡5(1)+5174056250sin⁡9(1)−28547481600sin⁡8(1)−39966474240sin⁡12(1)−4757913600sin⁡4(1)−14273740800sin⁡16(1)−86507520−951582720sin⁡20(1)+86507520sin⁡22(1)+4757913600sin⁡18(1)+951582720sin⁡2(1)+28547481600sin⁡14(1)+14273740800sin⁡6(1)+39966474240sin⁡10(1)\frac{88179 \log{\left(\sin{\left(1 \right)} + 1 \right)}}{1048576} - \frac{88179 \log{\left(1 - \sin{\left(1 \right)} \right)}}{1048576} - \frac{- 3424523520 \sin^{7}{\left(1 \right)} - 5503713280 \sin^{11}{\left(1 \right)} - 450357600 \sin^{3}{\left(1 \right)} - 2163862272 \sin^{15}{\left(1 \right)} - 155195040 \sin^{19}{\left(1 \right)} + 14549535 \sin^{21}{\left(1 \right)} + 749786037 \sin^{17}{\left(1 \right)} + 71957985 \sin{\left(1 \right)} + 4139920070 \sin^{13}{\left(1 \right)} + 1551313995 \sin^{5}{\left(1 \right)} + 5174056250 \sin^{9}{\left(1 \right)}}{- 28547481600 \sin^{8}{\left(1 \right)} - 39966474240 \sin^{12}{\left(1 \right)} - 4757913600 \sin^{4}{\left(1 \right)} - 14273740800 \sin^{16}{\left(1 \right)} - 86507520 - 951582720 \sin^{20}{\left(1 \right)} + 86507520 \sin^{22}{\left(1 \right)} + 4757913600 \sin^{18}{\left(1 \right)} + 951582720 \sin^{2}{\left(1 \right)} + 28547481600 \sin^{14}{\left(1 \right)} + 14273740800 \sin^{6}{\left(1 \right)} + 39966474240 \sin^{10}{\left(1 \right)}} 
-88179*log(1 - sin(1))/1048576 + 88179*log(1 + sin(1))/1048576 - (-5503713280*sin(1)^11 - 3424523520*sin(1)^7 - 2163862272*sin(1)^15 - 450357600*sin(1)^3 - 155195040*sin(1)^19 + 14549535*sin(1)^21 + 71957985*sin(1) + 749786037*sin(1)^17 + 1551313995*sin(1)^5 + 4139920070*sin(1)^13 + 5174056250*sin(1)^9)/(-86507520 - 39966474240*sin(1)^12 - 28547481600*sin(1)^8 - 14273740800*sin(1)^16 - 4757913600*sin(1)^4 - 951582720*sin(1)^20 + 86507520*sin(1)^22 + 951582720*sin(1)^2 + 4757913600*sin(1)^18 + 14273740800*sin(1)^6 + 28547481600*sin(1)^14 + 39966474240*sin(1)^10)
Respuesta numérica [src] 
42081.8030437732
42081.8030437732

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

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