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sin(x)/(1+cos^2(x))
Solving integrals/ sin(x)/(1+cos^2(x))

Integral of sin(x)/(1+cos^2(x)) dx

Limits of integration:

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The graph:

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Piecewise:

The solution

You have entered [src] 
  1               
  /               
 |                
 |     sin(x)     
 |  ----------- dx
 |         2      
 |  1 + cos (x)   
 |                
/                 
0
∫01sin⁡(x)cos⁡2(x)+1 dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)} + 1}\, dx 
Integral(sin(x)/(1 + cos(x)^2), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                 
 |                                  
 |    sin(x)                        
 | ----------- dx = C - atan(cos(x))
 |        2                         
 | 1 + cos (x)                      
 |                                  
/
∫sin⁡(x)cos⁡2(x)+1 dx=C−atan⁡(cos⁡(x))\int \frac{\sin{\left(x \right)}}{\cos^{2}{\left(x \right)} + 1}\, dx = C - \operatorname{atan}{\left(\cos{\left(x \right)} \right)}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.902-2
Plot the graph f(x)
The answer [src] 
                pi
-atan(cos(1)) + --
                4
−atan⁡(cos⁡(1))+π4- \operatorname{atan}{\left(\cos{\left(1 \right)} \right)} + \frac{\pi}{4} 
=
= 
                pi
-atan(cos(1)) + --
                4
−atan⁡(cos⁡(1))+π4- \operatorname{atan}{\left(\cos{\left(1 \right)} \right)} + \frac{\pi}{4} 
-atan(cos(1)) + pi/4
Numerical answer [src] 
0.290030874178775
0.290030874178775
The graph
Integral of sin(x)/(1+cos^2(x)) dx

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

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