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Integral of (1/cos^2x-sinx) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src]
  n                      
  -                      
  4                      
  /                      
 |                       
 |  /   1            \   
 |  |------- - sin(x)| dx
 |  |   2            |   
 |  \cos (x)         /   
 |                       
/                        
n                        
-                        
4                        
$$\int\limits_{\frac{n}{4}}^{\frac{n}{4}} \left(- \sin{\left(x \right)} + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx$$
Integral(1/(cos(x)^2) - sin(x), (x, n/4, n/4))
Detail solution
  1. Integrate term-by-term:

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

      1. The integral of sine is negative cosine:

      So, the result is:

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

      But the integral is

    The result is:

  2. Now simplify:

  3. Add the constant of integration:


The answer is:

The answer (Indefinite) [src]
  /                                           
 |                                            
 | /   1            \          sin(x)         
 | |------- - sin(x)| dx = C + ------ + cos(x)
 | |   2            |          cos(x)         
 | \cos (x)         /                         
 |                                            
/                                             
$$\int \left(- \sin{\left(x \right)} + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx = C + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} + \cos{\left(x \right)}$$
The answer [src]
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Numerical answer [src]
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    Use the examples entering the upper and lower limits of integration.