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sin^2x/cosx
Solving integrals/ sin^2x/cosx

Integral of sin^2x/cosx dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     2      
 |  sin (x)   
 |  ------- dx
 |   cos(x)   
 |            
/             
0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\, dx$$ 
Integral(sin(x)^2/cos(x), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                            
 |                                                             
 |    2                                                        
 | sin (x)          log(1 + sin(x))            log(-1 + sin(x))
 | ------- dx = C + --------------- - sin(x) - ----------------
 |  cos(x)                 2                          2        
 |                                                             
/
$$\int \frac{\sin^{2}{\left(x \right)}}{\cos{\left(x \right)}}\, dx = C - \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{2} + \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{2} - \sin{\left(x \right)}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
log(1 + sin(1))            log(1 - sin(1))
--------------- - sin(1) - ---------------
       2                          2
$$- \sin{\left(1 \right)} + \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{2} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{2}$$ 
=
= 
log(1 + sin(1))            log(1 - sin(1))
--------------- - sin(1) - ---------------
       2                          2
$$- \sin{\left(1 \right)} + \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{2} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{2}$$ 
log(1 + sin(1))/2 - sin(1) - log(1 - sin(1))/2
Numerical answer [src] 
0.384720186075621
0.384720186075621
The graph
Integral of sin^2x/cosx dx

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

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