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Identical expressions
tg(x)^ two +(ctg(x))^ two
tg(x) squared plus (ctg(x)) squared
tg(x) to the power of two plus (ctg(x)) to the power of two
tg(x)2+(ctg(x))2
tgx2+ctgx2
tg(x)²+(ctg(x))²
tg(x) to the power of 2+(ctg(x)) to the power of 2
tgx^2+ctgx^2
tg(x)^2+(ctg(x))^2dx
Similar expressions
tg(x)^2-(ctg(x))^2

Integral of tg(x)^2+(ctg(x))^2 dx

The solution

You have entered [src]

 pi                       
 --                       
 3                        
  /                       
 |                        
 |  /   2         2   \   
 |  \tan (x) + cot (x)/ dx
 |                        
/                         
pi                        
--                        
6

$$\int\limits_{\frac{\pi}{6}}^{\frac{\pi}{3}} \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)}\right)\, dx$$

Integral(tan(x)^2 + cot(x)^2, (x, pi/6, pi/3))

Detail solution

Integrate term-by-term:
1. Rewrite the integrand:
  
  $\tan^{2}{\left(x \right)} = \sec^{2}{\left(x \right)} - 1$
2. Integrate term-by-term:
  1. $\int \sec^{2}{\left(x \right)}\, dx = \tan{\left(x \right)}$
  1. The integral of a constant is the constant times the variable of integration:
    
    $\int \left(-1\right)\, dx = - x$
  The result is: $- x + \tan{\left(x \right)}$
1. Don't know the steps in finding this integral.
  
  But the integral is
  
  $- x - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
The result is: $- 2 x + \tan{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$
Now simplify:

$- 2 x + \tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}$
Add the constant of integration:

$- 2 x + \tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer is:

$- 2 x + \tan{\left(x \right)} - \frac{1}{\tan{\left(x \right)}}+ \mathrm{constant}$

The answer (Indefinite) [src]

  /                                                  
 |                                                   
 | /   2         2   \                cos(x)         
 | \tan (x) + cot (x)/ dx = C - 2*x - ------ + tan(x)
 |                                    sin(x)         
/

$$\int \left(\tan^{2}{\left(x \right)} + \cot^{2}{\left(x \right)}\right)\, dx = C - 2 x + \tan{\left(x \right)} - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

           ___
  pi   4*\/ 3 
- -- + -------
  3       3

$$- \frac{\pi}{3} + \frac{4 \sqrt{3}}{3}$$

           ___
  pi   4*\/ 3 
- -- + -------
  3       3

$$- \frac{\pi}{3} + \frac{4 \sqrt{3}}{3}$$

-pi/3 + 4*sqrt(3)/3

Numerical answer [src]

1.26220352556191

1.26220352556191

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

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Integral of tg(x)^2+(ctg(x))^2 dx

Limits of integration:

The graph:

Piecewise:

The solution