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Solving integrals/ tg^2x-ctg^2x

Integral of tg^2x-ctg^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 pi                       
 --                       
 4                        
  /                       
 |                        
 |  /   2         2   \   
 |  \tan (x) - cot (x)/ dx
 |                        
/                         
pi                        
--                        
6
$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{4}} \left(\tan^{2}{\left(x \right)} - \cot^{2}{\left(x \right)}\right)\, dx$$ 
Integral(tan(x)^2 - cot(x)^2, (x, pi/6, pi/4))
Detail solution

  1. Integrate term-by-term:

    1. Rewrite the integrand:

    2. Integrate term-by-term:

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

      The result is:

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

      1. Don't know the steps in finding this integral.

        But the integral is

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                            
 |                                             
 | /   2         2   \          cos(x)         
 | \tan (x) - cot (x)/ dx = C + ------ + tan(x)
 |                              sin(x)         
/
$$\int \left(\tan^{2}{\left(x \right)} - \cot^{2}{\left(x \right)}\right)\, dx = C + \tan{\left(x \right)} + \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
        ___
    4*\/ 3 
2 - -------
       3
$$2 - \frac{4 \sqrt{3}}{3}$$ 
=
= 
        ___
    4*\/ 3 
2 - -------
       3
$$2 - \frac{4 \sqrt{3}}{3}$$ 
2 - 4*sqrt(3)/3
Numerical answer [src] 
-0.309401076758503
-0.309401076758503

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

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