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Solving integrals/ 2/cos^2x+1

Integral of 2/cos^2x+1 dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                 
  /                 
 |                  
 |  /   2       \   
 |  |------- + 1| dx
 |  |   2       |   
 |  \cos (x)    /   
 |                  
/                   
-1
$$\int\limits_{-1}^{1} \left(1 + \frac{2}{\cos^{2}{\left(x \right)}}\right)\, dx$$ 
Integral(2/cos(x)^2 + 1, (x, -1, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of a constant is the constant times the variable of integration:

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

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

        But the integral is

      So, the result is:

    The result is:

  2. Now simplify:

  3. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                                   
 |                                    
 | /   2       \              2*sin(x)
 | |------- + 1| dx = C + x + --------
 | |   2       |               cos(x) 
 | \cos (x)    /                      
 |                                    
/
$$\int \left(1 + \frac{2}{\cos^{2}{\left(x \right)}}\right)\, dx = C + x + \frac{2 \sin{\left(x \right)}}{\cos{\left(x \right)}}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
    4*sin(1)
2 + --------
     cos(1)
$$2 + \frac{4 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$ 
=
= 
    4*sin(1)
2 + --------
     cos(1)
$$2 + \frac{4 \sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$ 
2 + 4*sin(1)/cos(1)
Numerical answer [src] 
8.22963089861961
8.22963089861961

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

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