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Solving integrals/ 1/(2sinx+sin2x)

Integral of 1/(2sinx+sin2x) dx

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The solution

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  1                         
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 |             1            
 |  1*------------------- dx
 |    2*sin(x) + sin(2*x)   
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0
∫011⋅12sin⁡(x)+sin⁡(2x) dx\int\limits_{0}^{1} 1 \cdot \frac{1}{2 \sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx 
Integral(1/(2*sin(x) + sin(2*x)), (x, 0, 1))
The answer (Indefinite) [src]
−(sin⁡2(2 x)+4 sin⁡x sin⁡(2 x)+cos⁡2(2 x)+(4 cos⁡x+2) cos⁡(2 x)+4 sin⁡2x+4 cos⁡2x+4 cos⁡x+1) log⁡(sin⁡2x+cos⁡2x+2 cos⁡x+1)+(−sin⁡2(2 x)−4 sin⁡x sin⁡(2 x)−cos⁡2(2 x)+(−4 cos⁡x−2) cos⁡(2 x)−4 sin⁡2x−4 cos⁡2x−4 cos⁡x−1) log⁡(sin⁡2x+cos⁡2x−2 cos⁡x+1)−4 sin⁡x sin⁡(2 x)−4 cos⁡x cos⁡(2 x)−8 sin⁡2x−8 cos⁡2x−4 cos⁡x8 sin⁡2(2 x)+32 sin⁡x sin⁡(2 x)+8 cos⁡2(2 x)+(32 cos⁡x+16) cos⁡(2 x)+32 sin⁡2x+32 cos⁡2x+32 cos⁡x+8-{{\left(\sin ^2\left(2\,x\right)+4\,\sin x\,\sin \left(2\,x\right) +\cos ^2\left(2\,x\right)+\left(4\,\cos x+2\right)\,\cos \left(2\,x \right)+4\,\sin ^2x+4\,\cos ^2x+4\,\cos x+1\right)\,\log \left(\sin ^2x+\cos ^2x+2\,\cos x+1\right)+\left(-\sin ^2\left(2\,x\right)-4\, \sin x\,\sin \left(2\,x\right)-\cos ^2\left(2\,x\right)+\left(-4\, \cos x-2\right)\,\cos \left(2\,x\right)-4\,\sin ^2x-4\,\cos ^2x-4\, \cos x-1\right)\,\log \left(\sin ^2x+\cos ^2x-2\,\cos x+1\right)-4\, \sin x\,\sin \left(2\,x\right)-4\,\cos x\,\cos \left(2\,x\right)-8\, \sin ^2x-8\,\cos ^2x-4\,\cos x}\over{8\,\sin ^2\left(2\,x\right)+32 \,\sin x\,\sin \left(2\,x\right)+8\,\cos ^2\left(2\,x\right)+\left( 32\,\cos x+16\right)\,\cos \left(2\,x\right)+32\,\sin ^2x+32\,\cos ^ 2x+32\,\cos x+8}}
Simplify
The answer [src] 
  1                       
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 |           1            
 |  ------------------- dx
 |  2*sin(x) + sin(2*x)   
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0
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  1                       
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 |           1            
 |  ------------------- dx
 |  2*sin(x) + sin(2*x)   
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0
∫0112sin⁡(x)+sin⁡(2x) dx\int\limits_{0}^{1} \frac{1}{2 \sin{\left(x \right)} + \sin{\left(2 x \right)}}\, dx
Simplify
Numerical answer [src] 
11.082058518454
11.082058518454

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

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