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- - **Many CAS not able to solve integral**
(*https://www.mersenneforum.org/showthread.php?t=8504*)

Many CAS not able to solve integralHello,
I tried(with wolfram integrator, mupad & derive) to solve this integral: SIN(x)·(1 - COS(x))· !!! ANGLES IN DEGREE!!! None of the three Computer Algebra Systems were able to do this correct(i set angle options). Can anybody help me? Thanks, Nuggetprime |

Let x be the angle in degrees, so the angle in radians is:
[tex]\frac{\pi}{180}x[/tex] So you want to integrate: [tex]\sin \left(\frac{\pi}{180}x\right)\left(1-cos(\frac{\pi}{180}x)\right)\,=\, \sin \left(\frac{\pi}{180}x\right)-\sin \left(\frac{\pi}{180}x\right)\,cos(\frac{\pi}{180}x)[/tex] using standard sin and cos functions in radian. Since [tex]\sin(2x) = 2\sin x \cos x[/tex] we get: [tex]\sin \left(\frac{\pi}{180}x\right)-\frac{1}{2}\sin \left(\frac{\pi}{90}x\right)[/tex] And its integral is: [tex]-\frac{180}{\pi}\cos \left(\frac{\pi}{180}x\right)+\frac{45}{\pi}\cos \left(\frac{\pi}{90}x\right)[/tex] So the result in degrees is (using cosines in degrees): [tex]-\frac{180}{\pi}\cos (x)+\frac{45}{\pi}\cos (2x)[/tex] I don't know the solution given by these packages but the difference between their results and the one I gave above should be a constant. Please notice that there are many ways to represent trigonometric identities so it is possible that two very different looking expressions are equal. |

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