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Hi Cbarker1,I am trying to integrate a difficult integrand.
\[1/2*\int \sin(\sqrt(3)/2x)*\sec(\sqrt(3)x)\, dx\]
I know that it requires to use integrate by parts.
Which function do I use to for the differential and integrable?
I am assuming that the first of Sudharaka's readings is the one that is intended: $\frac12{\displaystyle\int} \sin\bigl(\frac{\sqrt3}2x\bigr)\sec(\sqrt3x)\,dx$. If you write $$\sec(\sqrt3x) = \frac1{\cos(\sqrt3x)} = \frac1{2\cos^2 \bigl(\frac{\sqrt3}2x\bigr) -1}$$ and then make the substitution $u = \cos\bigl(\frac{\sqrt3}2x\bigr)$, the integral becomes $\displaystyle-\frac{\sqrt3}4 \int\frac{du}{2u^2-1}$, which you can integrate using partial fractions.I am trying to integrate a difficult integrand.
\[1/2*\int \sin(\sqrt(3)/2x)*\sec(\sqrt(3)x)\, dx\]
I know that it requires to use integrate by parts.
Which function do I use to for the differential and integrable?