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Solving integrals/ (-sin(x)*dx)/cos(x)

Integral of (-sin(x)*dx)/cos(x) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

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

  1. Let .

    Then let and substitute :

    1. The integral of is .

    Now substitute back in:

  2. Add the constant of integration:

The answer is:

The answer (Indefinite) [src] 
  /                             
 |                              
 | -sin(x)                      
 | -------- dx = C + log(cos(x))
 |  cos(x)                      
 |                              
/
$$\int \frac{\left(-1\right) \sin{\left(x \right)}}{\cos{\left(x \right)}}\, dx = C + \log{\left(\cos{\left(x \right)} \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(cos(1))
$$\log{\left(\cos{\left(1 \right)} \right)}$$ 
=
= 
log(cos(1))
$$\log{\left(\cos{\left(1 \right)} \right)}$$ 
log(cos(1))
Numerical answer [src] 
-0.615626470386014
-0.615626470386014

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

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