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Resolución de integrales/ cosh^3(x/5)

Integral de cosh^3(x/5) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  1            
  /            
 |             
 |      3/x\   
 |  cosh |-| dx
 |       \5/   
 |             
/              
0
∫01cosh⁡3(x5) dx\int\limits_{0}^{1} \cosh^{3}{\left(\frac{x}{5} \right)}\, dx 
Integral(cosh(x/5)^3, (x, 0, 1))
Respuesta (Indefinida) [src] 
  /                                         5/x \                                          /x \                                           3/x \                
 |                                   30*tanh |--|                                   30*tanh|--|                                    20*tanh |--|                
 |     3/x\                                  \10/                                          \10/                                            \10/                
 | cosh |-| dx = C - -------------------------------------------- - -------------------------------------------- + --------------------------------------------
 |      \5/                     4/x \         6/x \         2/x \              4/x \         6/x \         2/x \              4/x \         6/x \         2/x \
 |                   -3 - 9*tanh |--| + 3*tanh |--| + 9*tanh |--|   -3 - 9*tanh |--| + 3*tanh |--| + 9*tanh |--|   -3 - 9*tanh |--| + 3*tanh |--| + 9*tanh |--|
/                                \10/          \10/          \10/               \10/          \10/          \10/               \10/          \10/          \10/
∫cosh⁡3(x5) dx=C−30tanh⁡5(x10)3tanh⁡6(x10)−9tanh⁡4(x10)+9tanh⁡2(x10)−3+20tanh⁡3(x10)3tanh⁡6(x10)−9tanh⁡4(x10)+9tanh⁡2(x10)−3−30tanh⁡(x10)3tanh⁡6(x10)−9tanh⁡4(x10)+9tanh⁡2(x10)−3\int \cosh^{3}{\left(\frac{x}{5} \right)}\, dx = C - \frac{30 \tanh^{5}{\left(\frac{x}{10} \right)}}{3 \tanh^{6}{\left(\frac{x}{10} \right)} - 9 \tanh^{4}{\left(\frac{x}{10} \right)} + 9 \tanh^{2}{\left(\frac{x}{10} \right)} - 3} + \frac{20 \tanh^{3}{\left(\frac{x}{10} \right)}}{3 \tanh^{6}{\left(\frac{x}{10} \right)} - 9 \tanh^{4}{\left(\frac{x}{10} \right)} + 9 \tanh^{2}{\left(\frac{x}{10} \right)} - 3} - \frac{30 \tanh{\left(\frac{x}{10} \right)}}{3 \tanh^{6}{\left(\frac{x}{10} \right)} - 9 \tanh^{4}{\left(\frac{x}{10} \right)} + 9 \tanh^{2}{\left(\frac{x}{10} \right)} - 3}
Simplificar
Gráfica
0.001.000.100.200.300.400.500.600.700.800.9002
Trazar el gráfico f(x)
Respuesta [src] 
         3                              
  10*sinh (1/5)         2               
- ------------- + 5*cosh (1/5)*sinh(1/5)
        3
−10sinh⁡3(15)3+5sinh⁡(15)cosh⁡2(15)- \frac{10 \sinh^{3}{\left(\frac{1}{5} \right)}}{3} + 5 \sinh{\left(\frac{1}{5} \right)} \cosh^{2}{\left(\frac{1}{5} \right)} 
=
= 
         3                              
  10*sinh (1/5)         2               
- ------------- + 5*cosh (1/5)*sinh(1/5)
        3
−10sinh⁡3(15)3+5sinh⁡(15)cosh⁡2(15)- \frac{10 \sinh^{3}{\left(\frac{1}{5} \right)}}{3} + 5 \sinh{\left(\frac{1}{5} \right)} \cosh^{2}{\left(\frac{1}{5} \right)} 
-10*sinh(1/5)^3/3 + 5*cosh(1/5)^2*sinh(1/5)
Respuesta numérica [src] 
1.0202823354242
1.0202823354242

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

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