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Identical expressions
(tgx+ctgx)^ two
(tgx plus ctgx) squared
(tgx plus ctgx) to the power of two
(tgx+ctgx)2
tgx+ctgx2
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(tgx-ctgx)^2

Solving integrals/ (tgx+ctgx)^2

Integral of (tgx+ctgx)^2 dx

The solution

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  pi                      
  --                      
  4                       
   /                      
  |                       
  |                   2   
  |  (tan(x) + cot(x))  dx
  |                       
 /                        
-pi                       
----                      
 4

$$\int\limits_{- \frac{\pi}{4}}^{\frac{\pi}{4}} \left(\tan{\left(x \right)} + \cot{\left(x \right)}\right)^{2}\, dx$$

Integral((tan(x) + cot(x))^2, (x, -pi/4, pi/4))

Detail solution

Rewrite the integrand:

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

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

Simplify

The graph

Plot the graph f(x)

The answer [src]

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The graph

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

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Integral of (tgx+ctgx)^2 dx

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The solution