Integrate the following with respect to $x$
$$\int \frac{\cos(6x)+\cos(9x)}{1-\cos(5x)}.dx$$
Is this function integrable in terms of elementary functions? Could someone give me little hint to proceed in this question?
Integrate the following function with respect to $x$
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calculus
integration
indefinite-integrals
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0Hint : Use http://mathworld.wolfram.com/ProsthaphaeresisFormulas.html and $$\cos3y=\cos y(2\cos2y-1)$$ – 2017-02-15
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0In principle $\cos nx$ can be expressed as a polynomial in $\cos x$, and then the substitution $t=\tan \frac x2$ reduces this to the integral of a rational function. So yes is the answer, but this will undoubtedly not be the best way to proceed. – 2017-02-15
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0the solution looks terrible – 2017-02-15
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2See http://math.stackexchange.com/questions/1380072/help-with-primitive-function/1380080#1380080 http://math.stackexchange.com/questions/2106899/if-value-of-integral-is-given-then-find-k/2106920#2106920 http://math.stackexchange.com/questions/1817300/how-to-integrate-frac-cos-7x-cos-8x12-cos-5x/1831782#1831782 – 2017-02-15