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Resolución de integrales/ ch^2(x)/ sech^2(x)tanh^5(x)

Integral de sech^2(x)tanh^5(x) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  3                     
  /                     
 |                      
 |      2        5      
 |  sech (x)*tanh (x) dx
 |                      
/                       
2
$$\int\limits_{2}^{3} \tanh^{5}{\left(x \right)} \operatorname{sech}^{2}{\left(x \right)}\, dx$$ 
Integral(sech(x)^2*tanh(x)^5, (x, 2, 3))
Respuesta (Indefinida) [src] 
  /                                                                           
 |                                2          2        2          2        4   
 |     2        5             sech (x)   sech (x)*tanh (x)   sech (x)*tanh (x)
 | sech (x)*tanh (x) dx = C - -------- - ----------------- - -----------------
 |                               6               6                   6        
/
$$\int \tanh^{5}{\left(x \right)} \operatorname{sech}^{2}{\left(x \right)}\, dx = C - \frac{\tanh^{4}{\left(x \right)} \operatorname{sech}^{2}{\left(x \right)}}{6} - \frac{\tanh^{2}{\left(x \right)} \operatorname{sech}^{2}{\left(x \right)}}{6} - \frac{\operatorname{sech}^{2}{\left(x \right)}}{6}$$
Simplificar
Gráfica
Trazar el gráfico f(x)
Respuesta [src] 
      2          2          2        2          2        4          2        2          2        4   
  sech (3)   sech (2)   sech (3)*tanh (3)   sech (3)*tanh (3)   sech (2)*tanh (2)   sech (2)*tanh (2)
- -------- + -------- - ----------------- - ----------------- + ----------------- + -----------------
     6          6               6                   6                   6                   6
$$- \frac{\operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{2}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{4}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} + \frac{\tanh^{4}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\tanh^{2}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\operatorname{sech}^{2}{\left(2 \right)}}{6}$$ 
=
= 
      2          2          2        2          2        4          2        2          2        4   
  sech (3)   sech (2)   sech (3)*tanh (3)   sech (3)*tanh (3)   sech (2)*tanh (2)   sech (2)*tanh (2)
- -------- + -------- - ----------------- - ----------------- + ----------------- + -----------------
     6          6               6                   6                   6                   6
$$- \frac{\operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{2}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} - \frac{\tanh^{4}{\left(3 \right)} \operatorname{sech}^{2}{\left(3 \right)}}{6} + \frac{\tanh^{4}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\tanh^{2}{\left(2 \right)} \operatorname{sech}^{2}{\left(2 \right)}}{6} + \frac{\operatorname{sech}^{2}{\left(2 \right)}}{6}$$ 
-sech(3)^2/6 + sech(2)^2/6 - sech(3)^2*tanh(3)^2/6 - sech(3)^2*tanh(3)^4/6 + sech(2)^2*tanh(2)^2/6 + sech(2)^2*tanh(2)^4/6
Respuesta numérica [src] 
0.0280039096630232
0.0280039096630232

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

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