Mister Exam

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Similar expressions
(1/cos^2x+sinx)

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

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

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

$\cos{\left(x \right)} + \tan{\left(x \right)}$
Add the constant of integration:

$\cos{\left(x \right)} + \tan{\left(x \right)}+ \mathrm{constant}$

The answer is:

$\cos{\left(x \right)} + \tan{\left(x \right)}+ \mathrm{constant}$

The answer (Indefinite) [src]

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

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

Simplify

The answer [src]

$$0$$

Numerical answer [src]

0.0

0.0

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

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Identical expressions

Similar expressions

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

Limits of integration:

The graph:

Piecewise:

The solution