Mister Exam

Integral of th^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1            
  /            
 |             
 |      2      
 |  tanh (x) dx
 |             
/              
0              
$$\int\limits_{0}^{1} \tanh^{2}{\left(x \right)}\, dx$$
Integral(tanh(x)^2, (x, 0, 1))
Detail solution
  1. Let .

    Then let and substitute :

    1. The integral of a constant times a function is the constant times the integral of the function:

      1. Rewrite the integrand:

      2. Integrate term-by-term:

        1. The integral of a constant is the constant times the variable of integration:

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        1. The integral of a constant times a function is the constant times the integral of the function:

          1. Let .

            Then let and substitute :

            1. The integral of is .

            Now substitute back in:

          So, the result is:

        The result is:

      So, the result is:

    Now substitute back in:

  2. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                                                
 |                                                                 
 |     2             log(1 + tanh(x))             log(-1 + tanh(x))
 | tanh (x) dx = C + ---------------- - tanh(x) - -----------------
 |                          2                             2        
/                                                                  
$$\int \tanh^{2}{\left(x \right)}\, dx = C - \frac{\log{\left(\tanh{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\tanh{\left(x \right)} + 1 \right)}}{2} - \tanh{\left(x \right)}$$
The graph
The answer [src]
1 - tanh(1)
$$1 - \tanh{\left(1 \right)}$$
=
=
1 - tanh(1)
$$1 - \tanh{\left(1 \right)}$$
1 - tanh(1)
Numerical answer [src]
0.238405844044235
0.238405844044235
The graph
Integral of th^2x dx

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