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Resolución de integrales/ (2x-1)/ cos^3/ cos^3(2x-1)

Integral de cos^3(2x-1) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     3            
 |  cos (2*x - 1) dx
 |                  
/                   
0
∫01cos⁡3(2x−1) dx\int\limits_{0}^{1} \cos^{3}{\left(2 x - 1 \right)}\, dx 
Integral(cos(2*x - 1)^3, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                           
 |                                                  3                                                            5                                                                                            
 |    3                                        2*tan (-1/2 + x)                                             3*tan (-1/2 + x)                                             3*tan(-1/2 + x)                      
 | cos (2*x - 1) dx = C + ---------------------------------------------------------- + ---------------------------------------------------------- + ----------------------------------------------------------
 |                                 6                  2                  4                      6                  2                  4                      6                  2                  4          
/                         3 + 3*tan (-1/2 + x) + 9*tan (-1/2 + x) + 9*tan (-1/2 + x)   3 + 3*tan (-1/2 + x) + 9*tan (-1/2 + x) + 9*tan (-1/2 + x)   3 + 3*tan (-1/2 + x) + 9*tan (-1/2 + x) + 9*tan (-1/2 + x)
∫cos⁡3(2x−1) dx=C+3tan⁡5(x−12)3tan⁡6(x−12)+9tan⁡4(x−12)+9tan⁡2(x−12)+3+2tan⁡3(x−12)3tan⁡6(x−12)+9tan⁡4(x−12)+9tan⁡2(x−12)+3+3tan⁡(x−12)3tan⁡6(x−12)+9tan⁡4(x−12)+9tan⁡2(x−12)+3\int \cos^{3}{\left(2 x - 1 \right)}\, dx = C + \frac{3 \tan^{5}{\left(x - \frac{1}{2} \right)}}{3 \tan^{6}{\left(x - \frac{1}{2} \right)} + 9 \tan^{4}{\left(x - \frac{1}{2} \right)} + 9 \tan^{2}{\left(x - \frac{1}{2} \right)} + 3} + \frac{2 \tan^{3}{\left(x - \frac{1}{2} \right)}}{3 \tan^{6}{\left(x - \frac{1}{2} \right)} + 9 \tan^{4}{\left(x - \frac{1}{2} \right)} + 9 \tan^{2}{\left(x - \frac{1}{2} \right)} + 3} + \frac{3 \tan{\left(x - \frac{1}{2} \right)}}{3 \tan^{6}{\left(x - \frac{1}{2} \right)} + 9 \tan^{4}{\left(x - \frac{1}{2} \right)} + 9 \tan^{2}{\left(x - \frac{1}{2} \right)} + 3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-1
Trazar el gráfico f(x)
Respuesta [src] 
     3                    
2*sin (1)      2          
--------- + cos (1)*sin(1)
    3
sin⁡(1)cos⁡2(1)+2sin⁡3(1)3\sin{\left(1 \right)} \cos^{2}{\left(1 \right)} + \frac{2 \sin^{3}{\left(1 \right)}}{3} 
=
= 
     3                    
2*sin (1)      2          
--------- + cos (1)*sin(1)
    3
sin⁡(1)cos⁡2(1)+2sin⁡3(1)3\sin{\left(1 \right)} \cos^{2}{\left(1 \right)} + \frac{2 \sin^{3}{\left(1 \right)}}{3} 
2*sin(1)^3/3 + cos(1)^2*sin(1)
Respuesta numérica [src] 
0.642863239277578
0.642863239277578

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

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