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

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

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
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 |     2            
 |  cos (2*x - 1) dx
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0
∫01cos⁡2(2x−1) dx\int\limits_{0}^{1} \cos^{2}{\left(2 x - 1 \right)}\, dx 
Integral(cos(2*x - 1)^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                                                                                                                                                                                      
 |                                                                                                                            3                                          4                                          2                    
 |    2                                      x                                   tan(-1/2 + x)                             tan (-1/2 + x)                           x*tan (-1/2 + x)                         2*x*tan (-1/2 + x)          
 | cos (2*x - 1) dx = C + --------------------------------------- + --------------------------------------- - --------------------------------------- + --------------------------------------- + ---------------------------------------
 |                                 4                  2                      4                  2                      4                  2                      4                  2                      4                  2          
/                         2 + 2*tan (-1/2 + x) + 4*tan (-1/2 + x)   2 + 2*tan (-1/2 + x) + 4*tan (-1/2 + x)   2 + 2*tan (-1/2 + x) + 4*tan (-1/2 + x)   2 + 2*tan (-1/2 + x) + 4*tan (-1/2 + x)   2 + 2*tan (-1/2 + x) + 4*tan (-1/2 + x)
∫cos⁡2(2x−1) dx=C+xtan⁡4(x−12)2tan⁡4(x−12)+4tan⁡2(x−12)+2+2xtan⁡2(x−12)2tan⁡4(x−12)+4tan⁡2(x−12)+2+x2tan⁡4(x−12)+4tan⁡2(x−12)+2−tan⁡3(x−12)2tan⁡4(x−12)+4tan⁡2(x−12)+2+tan⁡(x−12)2tan⁡4(x−12)+4tan⁡2(x−12)+2\int \cos^{2}{\left(2 x - 1 \right)}\, dx = C + \frac{x \tan^{4}{\left(x - \frac{1}{2} \right)}}{2 \tan^{4}{\left(x - \frac{1}{2} \right)} + 4 \tan^{2}{\left(x - \frac{1}{2} \right)} + 2} + \frac{2 x \tan^{2}{\left(x - \frac{1}{2} \right)}}{2 \tan^{4}{\left(x - \frac{1}{2} \right)} + 4 \tan^{2}{\left(x - \frac{1}{2} \right)} + 2} + \frac{x}{2 \tan^{4}{\left(x - \frac{1}{2} \right)} + 4 \tan^{2}{\left(x - \frac{1}{2} \right)} + 2} - \frac{\tan^{3}{\left(x - \frac{1}{2} \right)}}{2 \tan^{4}{\left(x - \frac{1}{2} \right)} + 4 \tan^{2}{\left(x - \frac{1}{2} \right)} + 2} + \frac{\tan{\left(x - \frac{1}{2} \right)}}{2 \tan^{4}{\left(x - \frac{1}{2} \right)} + 4 \tan^{2}{\left(x - \frac{1}{2} \right)} + 2}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.902-1
Trazar el gráfico f(x)
Respuesta [src] 
   2         2                   
cos (1)   sin (1)   cos(1)*sin(1)
------- + ------- + -------------
   2         2            2
cos⁡2(1)2+sin⁡(1)cos⁡(1)2+sin⁡2(1)2\frac{\cos^{2}{\left(1 \right)}}{2} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\sin^{2}{\left(1 \right)}}{2} 
=
= 
   2         2                   
cos (1)   sin (1)   cos(1)*sin(1)
------- + ------- + -------------
   2         2            2
cos⁡2(1)2+sin⁡(1)cos⁡(1)2+sin⁡2(1)2\frac{\cos^{2}{\left(1 \right)}}{2} + \frac{\sin{\left(1 \right)} \cos{\left(1 \right)}}{2} + \frac{\sin^{2}{\left(1 \right)}}{2} 
cos(1)^2/2 + sin(1)^2/2 + cos(1)*sin(1)/2
Respuesta numérica [src] 
0.72732435670642
0.72732435670642

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

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