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  • Identical expressions

  • sin2(x)/(cos(x)^ three)
  • sinus of 2(x) divide by ( co sinus of e of (x) cubed )
  • sinus of 2(x) divide by ( co sinus of e of (x) to the power of three)
  • sin2(x)/(cos(x)3)
  • sin2x/cosx3
  • sin2(x)/(cos(x)³)
  • sin2(x)/(cos(x) to the power of 3)
  • sin2x/cosx^3
  • sin2(x) divide by (cos(x)^3)
  • sin2(x)/(cos(x)^3)dx

  • Similar expressions

  • sin2(x)/(cosx^3)
Solving integrals/ sin2(x)/(cos(x)^3)

Integral of sin2(x)/(cos(x)^3) dx

Limits of integration:

from to
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     2      
 |  sin (x)   
 |  ------- dx
 |     3      
 |  cos (x)   
 |            
/             
0
$$\int\limits_{0}^{1} \frac{\sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}}\, dx$$ 
Integral(sin(x)^2/cos(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                                                                     
 |    2                                                                
 | sin (x)          log(1 + sin(x))   log(-1 + sin(x))       sin(x)    
 | ------- dx = C - --------------- + ---------------- - --------------
 |    3                    4                 4                     2   
 | cos (x)                                               -2 + 2*sin (x)
 |                                                                     
/
$$\int \frac{\sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}}\, dx = C + \frac{\log{\left(\sin{\left(x \right)} - 1 \right)}}{4} - \frac{\log{\left(\sin{\left(x \right)} + 1 \right)}}{4} - \frac{\sin{\left(x \right)}}{2 \sin^{2}{\left(x \right)} - 2}$$
Simplify
The graph
Plot the graph f(x)
The answer [src] 
  log(1 + sin(1))   log(1 - sin(1))       sin(1)    
- --------------- + --------------- - --------------
         4                 4                    2   
                                      -2 + 2*sin (1)
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}}$$ 
=
= 
  log(1 + sin(1))   log(1 - sin(1))       sin(1)    
- --------------- + --------------- - --------------
         4                 4                    2   
                                      -2 + 2*sin (1)
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}}$$ 
-log(1 + sin(1))/4 + log(1 - sin(1))/4 - sin(1)/(-2 + 2*sin(1)^2)
Numerical answer [src] 
0.828141762372732
0.828141762372732

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

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