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Resolución de integrales/ cos^2/ loge(x)/ cos^2(loge(x))

Integral de cos^2(loge(x)) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1                 
  /                 
 |                  
 |     2/ log(x)\   
 |  cos |-------| dx
 |      |   / 1\|   
 |      \log\e //   
 |                  
/                   
0
∫01cos⁡2(log⁡(x)log⁡(e1)) dx\int\limits_{0}^{1} \cos^{2}{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}} \right)}\, dx 
Integral(cos(log(x)/log(exp(1)))^2, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                                                               3/log(x)\                              2/log(x)\                              4/log(x)\                              /log(x)\           
 |                                                                         4*x*tan |------|                       2*x*tan |------|                       3*x*tan |------|                       4*x*tan|------|           
 |    2/ log(x)\                          3*x                                      \  2   /                               \  2   /                               \  2   /                              \  2   /           
 | cos |-------| dx = C + ------------------------------------ - ------------------------------------ + ------------------------------------ + ------------------------------------ + ------------------------------------
 |     |   / 1\|                   4/log(x)\         2/log(x)\            4/log(x)\         2/log(x)\            4/log(x)\         2/log(x)\            4/log(x)\         2/log(x)\            4/log(x)\         2/log(x)\
 |     \log\e //          5 + 5*tan |------| + 10*tan |------|   5 + 5*tan |------| + 10*tan |------|   5 + 5*tan |------| + 10*tan |------|   5 + 5*tan |------| + 10*tan |------|   5 + 5*tan |------| + 10*tan |------|
 |                                  \  2   /          \  2   /             \  2   /          \  2   /             \  2   /          \  2   /             \  2   /          \  2   /             \  2   /          \  2   /
/
∫cos⁡2(log⁡(x)log⁡(e1)) dx=C+3xtan⁡4(log⁡(x)2)5tan⁡4(log⁡(x)2)+10tan⁡2(log⁡(x)2)+5−4xtan⁡3(log⁡(x)2)5tan⁡4(log⁡(x)2)+10tan⁡2(log⁡(x)2)+5+2xtan⁡2(log⁡(x)2)5tan⁡4(log⁡(x)2)+10tan⁡2(log⁡(x)2)+5+4xtan⁡(log⁡(x)2)5tan⁡4(log⁡(x)2)+10tan⁡2(log⁡(x)2)+5+3x5tan⁡4(log⁡(x)2)+10tan⁡2(log⁡(x)2)+5\int \cos^{2}{\left(\frac{\log{\left(x \right)}}{\log{\left(e^{1} \right)}} \right)}\, dx = C + \frac{3 x \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} - \frac{4 x \tan^{3}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} + \frac{2 x \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} + \frac{4 x \tan{\left(\frac{\log{\left(x \right)}}{2} \right)}}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5} + \frac{3 x}{5 \tan^{4}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 10 \tan^{2}{\left(\frac{\log{\left(x \right)}}{2} \right)} + 5}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
3/5
35\frac{3}{5} 
=
= 
3/5
35\frac{3}{5} 
3/5
Respuesta numérica [src] 
0.6
0.6

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

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