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sec^3
Solving integrals/ sec^3

Integral of sec^3 dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1           
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 |     3      
 |  sec (x) dx
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0
∫01sec⁡3(x) dx\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⁡(sin⁡x+1)4−log⁡(sin⁡x−1)4−sin⁡x2 sin⁡2x−2{{\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
0.001.000.100.200.300.400.500.600.700.800.90010
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⁡(sin⁡1+1)4−log⁡(1−sin⁡1)4−sin⁡12 sin⁡21−2{{\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)
log⁡(sin⁡(1)+1)4−log⁡(1−sin⁡(1))4−sin⁡(1)−2+2sin⁡2(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)}}
Упростить
Numerical answer [src] 
2.05433293325625
2.05433293325625
The graph
Integral of sec^3 dx

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

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