Mister Exam

Other calculators

  • How to use it?

  • Integral of d{x}:
  • Integral of k Integral of k
  • Integral of -y Integral of -y
  • Integral of x*e^(2*x)*dx Integral of x*e^(2*x)*dx
  • Integral of (1-x^2)^(1/2) Integral of (1-x^2)^(1/2)

  • Identical expressions

  • a*sinh(x)*tanh(x)/(a^ two +(b+cosh(x))^ two)
  • a multiply by hyperbolic sinus of e of (x) multiply by hyperbolic tangent of gent of (x) divide by (a squared plus (b plus hyperbolic co sinus of e of ine of (x)) squared )
  • a multiply by hyperbolic sinus of e of (x) multiply by hyperbolic tangent of gent of (x) divide by (a to the power of two plus (b plus hyperbolic co sinus of e of ine of (x)) to the power of two)
  • a*sinh(x)*tanh(x)/(a2+(b+cosh(x))2)
  • a*sinhx*tanhx/a2+b+coshx2
  • a*sinh(x)*tanh(x)/(a²+(b+cosh(x))²)
  • a*sinh(x)*tanh(x)/(a to the power of 2+(b+cosh(x)) to the power of 2)
  • asinh(x)tanh(x)/(a^2+(b+cosh(x))^2)
  • asinh(x)tanh(x)/(a2+(b+cosh(x))2)
  • asinhxtanhx/a2+b+coshx2
  • asinhxtanhx/a^2+b+coshx^2
  • a*sinh(x)*tanh(x) divide by (a^2+(b+cosh(x))^2)
  • a*sinh(x)*tanh(x)/(a^2+(b+cosh(x))^2)dx

  • Similar expressions

  • a*sinh(x)*tanh(x)/(a^2-(b+cosh(x))^2)
  • a*sinh(x)*tanh(x)/(a^2+(b-cosh(x))^2)
Solving integrals/ a*sinh(x)*tanh(x)/(a^2+(b+cosh(x))^2)

Integral of a*sinh(x)*tanh(x)/(a^2+(b+cosh(x))^2) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 oo                       
  /                       
 |                        
 |   a*sinh(x)*tanh(x)    
 |  ------------------- dx
 |   2                2   
 |  a  + (b + cosh(x))    
 |                        
/                         
-oo
$$\int\limits_{-\infty}^{\infty} \frac{a \sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + \left(b + \cosh{\left(x \right)}\right)^{2}}\, dx$$ 
Integral(((a*sinh(x))*tanh(x))/(a^2 + (b + cosh(x))^2), (x, -oo, oo))
The answer (Indefinite) [src] 
  /                                 /                                   
 |                                 |                                    
 |  a*sinh(x)*tanh(x)              |         sinh(x)*tanh(x)            
 | ------------------- dx = C + a* | -------------------------------- dx
 |  2                2             |  2    2       2                    
 | a  + (b + cosh(x))              | a  + b  + cosh (x) + 2*b*cosh(x)   
 |                                 |                                    
/                                 /
$$\int \frac{a \sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + \left(b + \cosh{\left(x \right)}\right)^{2}}\, dx = C + a \int \frac{\sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + b^{2} + 2 b \cosh{\left(x \right)} + \cosh^{2}{\left(x \right)}}\, dx$$
Simplify
The answer [src] 
   oo                                    
    /                                    
   |                                     
   |          sinh(x)*tanh(x)            
a* |  -------------------------------- dx
   |   2    2       2                    
   |  a  + b  + cosh (x) + 2*b*cosh(x)   
   |                                     
  /                                      
  -oo
$$a \int\limits_{-\infty}^{\infty} \frac{\sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + b^{2} + 2 b \cosh{\left(x \right)} + \cosh^{2}{\left(x \right)}}\, dx$$ 
=
= 
   oo                                    
    /                                    
   |                                     
   |          sinh(x)*tanh(x)            
a* |  -------------------------------- dx
   |   2    2       2                    
   |  a  + b  + cosh (x) + 2*b*cosh(x)   
   |                                     
  /                                      
  -oo
$$a \int\limits_{-\infty}^{\infty} \frac{\sinh{\left(x \right)} \tanh{\left(x \right)}}{a^{2} + b^{2} + 2 b \cosh{\left(x \right)} + \cosh^{2}{\left(x \right)}}\, dx$$ 
a*Integral(sinh(x)*tanh(x)/(a^2 + b^2 + cosh(x)^2 + 2*b*cosh(x)), (x, -oo, oo))

    Use the examples entering the upper and lower limits of integration.

    © Mister Exam – Calculator