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Similar expressions
2+1/cos^2x

Solving integrals/ 2-1/cos^2x

Integral of 2-1/cos^2x dx

The solution

You have entered [src]

  1                   
  /                   
 |                    
 |  /         1   \   
 |  |2 - 1*-------| dx
 |  |         2   |   
 |  \      cos (x)/   
 |                    
/                     
0

$$\int\limits_{0}^{1} \left(2 - 1 \cdot \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx$$

Integral(2 - 1/(cos(x)^2), (x, 0, 1))

Detail solution

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

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

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

The answer is:

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

The answer (Indefinite) [src]

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

$$2\,x-\tan x$$

Simplify

The graph

Plot the graph f(x)

The answer [src]

    sin(1)
2 - ------
    cos(1)

$$2-\tan 1$$

    sin(1)
2 - ------
    cos(1)

$$- \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}} + 2$$

Simplify

Numerical answer [src]

0.442592275345098

0.442592275345098

The graph

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

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Identical expressions

Similar expressions

Integral of 2-1/cos^2x dx

Limits of integration:

The graph:

Piecewise:

The solution