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sinx/(sinx+cosx)
Solving integrals/ sinx/(sinx+cosx)

Integral of sinx/(sinx+cosx) 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
 |  sin(x) + cos(x)   
 |                    
/                     
0
∫01sin⁡(x)sin⁡(x)+cos⁡(x) dx\int\limits_{0}^{1} \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx 
Integral(sin(x)/(sin(x) + cos(x)), (x, 0, 1))
The answer (Indefinite) [src] 
  /                                                 
 |                                                  
 |      sin(x)              x   log(cos(x) + sin(x))
 | --------------- dx = C + - - --------------------
 | sin(x) + cos(x)          2            2          
 |                                                  
/
∫sin⁡(x)sin⁡(x)+cos⁡(x) dx=C+x2−log⁡(sin⁡(x)+cos⁡(x))2\int \frac{\sin{\left(x \right)}}{\sin{\left(x \right)} + \cos{\left(x \right)}}\, dx = C + \frac{x}{2} - \frac{\log{\left(\sin{\left(x \right)} + \cos{\left(x \right)} \right)}}{2}
Simplify
The graph
0.001.000.100.200.300.400.500.600.700.800.900.01.0
Plot the graph f(x)
The answer [src] 
1   log(cos(1) + sin(1))
- - --------------------
2            2
12−log⁡(cos⁡(1)+sin⁡(1))2\frac{1}{2} - \frac{\log{\left(\cos{\left(1 \right)} + \sin{\left(1 \right)} \right)}}{2} 
=
= 
1   log(cos(1) + sin(1))
- - --------------------
2            2
12−log⁡(cos⁡(1)+sin⁡(1))2\frac{1}{2} - \frac{\log{\left(\cos{\left(1 \right)} + \sin{\left(1 \right)} \right)}}{2} 
1/2 - log(cos(1) + sin(1))/2
Numerical answer [src] 
0.338316166242309
0.338316166242309
The graph
Integral of sinx/(sinx+cosx) dx

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

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