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Integral of (dx)/(2*sin(x)+cos(x)) dx

Limits of integration:

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The solution

You have entered [src]
  1                     
  /                     
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 |          1           
 |  ----------------- dx
 |  2*sin(x) + cos(x)   
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0                       
$$\int\limits_{0}^{1} \frac{1}{2 \sin{\left(x \right)} + \cos{\left(x \right)}}\, dx$$
Integral(1/(2*sin(x) + cos(x)), (x, 0, 1))
The graph
The answer [src]
    ___ /          /      ___           \\     ___    /       ___\     ___ /          /      ___\\     ___    /       ___           \
  \/ 5 *\pi*I + log\2 + \/ 5  - tan(1/2)//   \/ 5 *log\-2 + \/ 5 /   \/ 5 *\pi*I + log\2 + \/ 5 //   \/ 5 *log\-2 + \/ 5  + tan(1/2)/
- ---------------------------------------- - --------------------- + ----------------------------- + --------------------------------
                     5                                 5                           5                                5                
$$\frac{\sqrt{5} \log{\left(-2 + \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(-2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 2 + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)}{5}$$
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    ___ /          /      ___           \\     ___    /       ___\     ___ /          /      ___\\     ___    /       ___           \
  \/ 5 *\pi*I + log\2 + \/ 5  - tan(1/2)//   \/ 5 *log\-2 + \/ 5 /   \/ 5 *\pi*I + log\2 + \/ 5 //   \/ 5 *log\-2 + \/ 5  + tan(1/2)/
- ---------------------------------------- - --------------------- + ----------------------------- + --------------------------------
                     5                                 5                           5                                5                
$$\frac{\sqrt{5} \log{\left(-2 + \tan{\left(\frac{1}{2} \right)} + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \log{\left(-2 + \sqrt{5} \right)}}{5} - \frac{\sqrt{5} \left(\log{\left(- \tan{\left(\frac{1}{2} \right)} + 2 + \sqrt{5} \right)} + i \pi\right)}{5} + \frac{\sqrt{5} \left(\log{\left(2 + \sqrt{5} \right)} + i \pi\right)}{5}$$
-sqrt(5)*(pi*i + log(2 + sqrt(5) - tan(1/2)))/5 - sqrt(5)*log(-2 + sqrt(5))/5 + sqrt(5)*(pi*i + log(2 + sqrt(5)))/5 + sqrt(5)*log(-2 + sqrt(5) + tan(1/2))/5
Numerical answer [src]
0.597603093483765
0.597603093483765

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