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sec^3x
Solving integrals/ sec^3x

Integral of sec^3x dx

Limits of integration:

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Piecewise:

The solution

You have entered [src] 
  1           
  /           
 |            
 |     3      
 |  sec (x) dx
 |            
/             
0
$$\int\limits_{0}^{1} \sec^{3}{\left(x \right)}\, dx$$ 
Integral(sec(x)^3, (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                                    
 |                                                                     
 |    3             log(-1 + sin(x))   log(1 + sin(x))       sin(x)    
 | sec (x) dx = C - ---------------- + --------------- - --------------
 |                         4                  4                    2   
/                                                        -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)
$$\frac{\log{\left(\sin{\left(1 \right)} + 1 \right)}}{4} - \frac{\log{\left(1 - \sin{\left(1 \right)} \right)}}{4} - \frac{\sin{\left(1 \right)}}{-2 + 2 \sin^{2}{\left(1 \right)}}$$
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Numerical answer [src] 
2.05433293325625
2.05433293325625
The graph
Integral of sec^3x dx

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

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