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1-cot^2(x)

Integral of 1+cot^2(x) dx

The solution

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 pi                 
 --                 
 2                  
  /                 
 |                  
 |  /       2   \   
 |  \1 + cot (x)/ dx
 |                  
/                   
pi                  
--                  
4

$$\int\limits_{\frac{\pi}{4}}^{\frac{\pi}{2}} \left(\cot^{2}{\left(x \right)} + 1\right)\, dx$$

Integral(1 + cot(x)^2, (x, pi/4, pi/2))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

  /                             
 |                              
 | /       2   \          cos(x)
 | \1 + cot (x)/ dx = C - ------
 |                        sin(x)
/

$$\int \left(\cot^{2}{\left(x \right)} + 1\right)\, dx = C - \frac{\cos{\left(x \right)}}{\sin{\left(x \right)}}$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

$$1$$

Numerical answer [src]

1.0

1.0

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

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Identical expressions

Similar expressions

Integral of 1+cot^2(x) dx

Limits of integration:

The graph:

Piecewise:

The solution