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  • Identical expressions

  • three -tg^ two (x/ three)/sin^ two (x/ three)
  • 3 minus tg squared (x divide by 3) divide by sinus of squared (x divide by 3)
  • three minus tg to the power of two (x divide by three) divide by sinus of to the power of two (x divide by three)
  • 3-tg2(x/3)/sin2(x/3)
  • 3-tg2x/3/sin2x/3
  • 3-tg²(x/3)/sin²(x/3)
  • 3-tg to the power of 2(x/3)/sin to the power of 2(x/3)
  • 3-tg^2x/3/sin^2x/3
  • 3-tg^2(x divide by 3) divide by sin^2(x divide by 3)
  • 3-tg^2(x/3)/sin^2(x/3)dx

  • Similar expressions

  • 3+tg^2(x/3)/sin^2(x/3)
Solving integrals/ 3-tg^2(x/3)/sin^2(x/3)

Integral of 3-tg^2(x/3)/sin^2(x/3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  /       2/x\\   
 |  |    tan |-||   
 |  |        \3/|   
 |  |3 - -------| dx
 |  |       2/x\|   
 |  |    sin |-||   
 |  \        \3//   
 |                  
/                   
0
$$\int\limits_{0}^{1} \left(3 - \frac{\tan^{2}{\left(\frac{x}{3} \right)}}{\sin^{2}{\left(\frac{x}{3} \right)}}\right)\, dx$$ 
Integral(3 - tan(x/3)^2/sin(x/3)^2, (x, 0, 1))
Detail solution

  1. 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. 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/x\\                     /x\
 | |    tan |-||                3*sin|-|
 | |        \3/|                     \3/
 | |3 - -------| dx = C + 3*x - --------
 | |       2/x\|                    /x\ 
 | |    sin |-||                 cos|-| 
 | \        \3//                    \3/ 
 |                                      
/
$$\int \left(3 - \frac{\tan^{2}{\left(\frac{x}{3} \right)}}{\sin^{2}{\left(\frac{x}{3} \right)}}\right)\, dx = C + 3 x - \frac{3 \sin{\left(\frac{x}{3} \right)}}{\cos{\left(\frac{x}{3} \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    3*sin(1/3)
3 - ----------
     cos(1/3)
$$- \frac{3 \sin{\left(\frac{1}{3} \right)}}{\cos{\left(\frac{1}{3} \right)}} + 3$$ 
=
= 
    3*sin(1/3)
3 - ----------
     cos(1/3)
$$- \frac{3 \sin{\left(\frac{1}{3} \right)}}{\cos{\left(\frac{1}{3} \right)}} + 3$$ 
3 - 3*sin(1/3)/cos(1/3)
Numerical answer [src] 
1.96123935146827
1.96123935146827

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

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