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  • Expresiones idénticas

  • ((coshx)^ cuatro)*((sinhx)^ dos)
  • (( coseno de eno hiperbólico de x) en el grado 4) multiplicar por (( seno hiperbólico de x) al cuadrado )
  • (( coseno de eno hiperbólico de x) en el grado cuatro) multiplicar por (( seno hiperbólico de x) en el grado dos)
  • ((coshx)4)*((sinhx)2)
  • coshx4*sinhx2
  • ((coshx)⁴)*((sinhx)²)
  • ((coshx) en el grado 4)*((sinhx) en el grado 2)
  • ((coshx)^4)((sinhx)^2)
  • ((coshx)4)((sinhx)2)
  • coshx4sinhx2
  • coshx^4sinhx^2
  • ((coshx)^4)*((sinhx)^2)dx
  • Expresiones con funciones

  • sinhx
  • sinhx/(1+tanshx)

Integral de ((coshx)^4)*((sinhx)^2) dx

Límites de integración:

interior superior
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  1                     
  /                     
 |                      
 |      4        2      
 |  cosh (x)*sinh (x) dx
 |                      
/                       
0                       
$$\int\limits_{0}^{1} \sinh^{2}{\left(x \right)} \cosh^{4}{\left(x \right)}\, dx$$
Integral(cosh(x)^4*sinh(x)^2, (x, 0, 1))
Respuesta (Indefinida) [src]
  /                                                                                                                                                            
 |                                  6          5                  3        3            6          5                      2        4              4        2   
 |     4        2             x*cosh (x)   sinh (x)*cosh(x)   cosh (x)*sinh (x)   x*sinh (x)   cosh (x)*sinh(x)   3*x*cosh (x)*sinh (x)   3*x*cosh (x)*sinh (x)
 | cosh (x)*sinh (x) dx = C - ---------- - ---------------- + ----------------- + ---------- + ---------------- - --------------------- + ---------------------
 |                                16              16                  6               16              16                    16                      16         
/                                                                                                                                                              
$$\int \sinh^{2}{\left(x \right)} \cosh^{4}{\left(x \right)}\, dx = C + \frac{x \sinh^{6}{\left(x \right)}}{16} - \frac{3 x \sinh^{4}{\left(x \right)} \cosh^{2}{\left(x \right)}}{16} + \frac{3 x \sinh^{2}{\left(x \right)} \cosh^{4}{\left(x \right)}}{16} - \frac{x \cosh^{6}{\left(x \right)}}{16} - \frac{\sinh^{5}{\left(x \right)} \cosh{\left(x \right)}}{16} + \frac{\sinh^{3}{\left(x \right)} \cosh^{3}{\left(x \right)}}{6} + \frac{\sinh{\left(x \right)} \cosh^{5}{\left(x \right)}}{16}$$
Gráfica
Respuesta [src]
      6          6            2        4          5                  3        3          5                    4        2   
  cosh (1)   sinh (1)   3*cosh (1)*sinh (1)   sinh (1)*cosh(1)   cosh (1)*sinh (1)   cosh (1)*sinh(1)   3*cosh (1)*sinh (1)
- -------- + -------- - ------------------- - ---------------- + ----------------- + ---------------- + -------------------
     16         16               16                  16                  6                  16                   16        
$$- \frac{3 \sinh^{4}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{16} - \frac{\cosh^{6}{\left(1 \right)}}{16} - \frac{\sinh^{5}{\left(1 \right)} \cosh{\left(1 \right)}}{16} + \frac{\sinh^{6}{\left(1 \right)}}{16} + \frac{\sinh{\left(1 \right)} \cosh^{5}{\left(1 \right)}}{16} + \frac{\sinh^{3}{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{6} + \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{4}{\left(1 \right)}}{16}$$
=
=
      6          6            2        4          5                  3        3          5                    4        2   
  cosh (1)   sinh (1)   3*cosh (1)*sinh (1)   sinh (1)*cosh(1)   cosh (1)*sinh (1)   cosh (1)*sinh(1)   3*cosh (1)*sinh (1)
- -------- + -------- - ------------------- - ---------------- + ----------------- + ---------------- + -------------------
     16         16               16                  16                  6                  16                   16        
$$- \frac{3 \sinh^{4}{\left(1 \right)} \cosh^{2}{\left(1 \right)}}{16} - \frac{\cosh^{6}{\left(1 \right)}}{16} - \frac{\sinh^{5}{\left(1 \right)} \cosh{\left(1 \right)}}{16} + \frac{\sinh^{6}{\left(1 \right)}}{16} + \frac{\sinh{\left(1 \right)} \cosh^{5}{\left(1 \right)}}{16} + \frac{\sinh^{3}{\left(1 \right)} \cosh^{3}{\left(1 \right)}}{6} + \frac{3 \sinh^{2}{\left(1 \right)} \cosh^{4}{\left(1 \right)}}{16}$$
-cosh(1)^6/16 + sinh(1)^6/16 - 3*cosh(1)^2*sinh(1)^4/16 - sinh(1)^5*cosh(1)/16 + cosh(1)^3*sinh(1)^3/6 + cosh(1)^5*sinh(1)/16 + 3*cosh(1)^4*sinh(1)^2/16
Respuesta numérica [src]
1.35782462363605
1.35782462363605

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