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sin^2x/cos^3(x)

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  • Integral of d{x}:
  • Integral of xe Integral of xe
  • Integral of 3x² Integral of 3x²
  • Integral of e^-t Integral of e^-t
  • Integral of e^(x*y)

  • Identical expressions

  • sin^2x/cos^ three (x)
  • sinus of squared x divide by co sinus of e of cubed (x)
  • sinus of squared x divide by co sinus of e of to the power of three (x)
  • sin2x/cos3(x)
  • sin2x/cos3x
  • sin²x/cos³(x)
  • sin to the power of 2x/cos to the power of 3(x)
  • sin^2x/cos^3x
  • sin^2x divide by cos^3(x)
  • sin^2x/cos^3(x)dx
Solving integrals/ sin^2x/cos^3(x)

Integral of sin^2x/cos^3(x) dx

Limits of integration:

from to
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The graph:

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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)
 |                                                                     
/
$$-{{\log \left(\sin x+1\right)}\over{4}}+{{\log \left(\sin x-1 \right)}\over{4}}-{{\sin x}\over{2\,\sin ^2x-2}}$$
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)
$$-{{\log \left(\sin 1+1\right)}\over{4}}+{{\log \left(1-\sin 1 \right)}\over{4}}-{{\sin 1}\over{2\,\sin ^21-2}}$$ 
=
= 
  log(1 + sin(1))   log(1 - sin(1))       sin(1)    
- --------------- + --------------- - --------------
         4                 4                    2   
                                      -2 + 2*sin (1)
$$\frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}}$$
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Numerical answer [src] 
0.828141762372732
0.828141762372732
The graph
Integral of sin^2x/cos^3(x) dx

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

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