## EscherichiaRinku 4 years ago Need some help integrating this and finding the coefficients (one given here as c and other comes from integration). $y = \frac{c}{2}\int\limits \frac{1}{1-\sin^3(3x)}dx$ with following boundary constraints: $y(-\frac{\pi}{12})=\frac{1}{2},\ y(\frac{\pi}{12})=\frac{3}{2}$ I can't believe this is an exam exercise, it's takes too long to solve it than it's worth the points >.<

1. anonymous

my guess is that you cannot find a nice closed form for this integral, but i will be quiet and let a smarter person try

2. EscherichiaRinku

I tried both substituting the denominator or substitute sin(3x), but both ways that one resulted in a way too long formula x_x;

3. anonymous

have you integrated this?

4. EscherichiaRinku

my simpler result our of two looks like this: $-\frac{9c}{4}(\sin^2(3x)cox(3x))+\frac{1}{4}(\ln(1-\sin^3(3x))+\frac{1}{2}K$ and its quite a mess to find the constants. I wonder if this integration result is even correct o.0

5. anonymous

is this complete and full and final result?

6. EscherichiaRinku

The integration is complete (not necesarily without errors) and this still needs the constants c and K, which are also quite a pain to find :(