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sinx+1/cos^2x
Solving integrals/ sinx+1/cos^2x

Integral of sinx+1/cos^2x dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1                      
  /                      
 |                       
 |  /            1   \   
 |  |sin(x) + -------| dx
 |  |            2   |   
 |  \         cos (x)/   
 |                       
/                        
0
$$\int\limits_{0}^{1} \left(\sin{\left(x \right)} + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx$$ 
Integral(sin(x) + 1/(cos(x)^2), (x, 0, 1))
Detail solution

  1. Integrate term-by-term:

    1. The integral of sine is negative cosine:

    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)/                         
 |                                            
/
$$\int \left(\sin{\left(x \right)} + \frac{1}{\cos^{2}{\left(x \right)}}\right)\, dx = C + \frac{\sin{\left(x \right)}}{\cos{\left(x \right)}} - \cos{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
             sin(1)
1 - cos(1) + ------
             cos(1)
$$- \cos{\left(1 \right)} + 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$ 
=
= 
             sin(1)
1 - cos(1) + ------
             cos(1)
$$- \cos{\left(1 \right)} + 1 + \frac{\sin{\left(1 \right)}}{\cos{\left(1 \right)}}$$ 
1 - cos(1) + sin(1)/cos(1)
Numerical answer [src] 
2.01710541878676
2.01710541878676
The graph
Integral of sinx+1/cos^2x dx

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

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