I have calculated the antiderivative of $sin^n(x)$ from $n=1$ to $n=20$ by software. Now I want to know if there are some laws about them？
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https://math.stackexchange.com/questions/112687/integrating-int-sinnx-dx – Matti P. Nov 06 '19 at 08:41
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I added a answer to the linked question: if $I_n(x) =\int \sin^n(x)dx $, then $I_{n}(x) =\frac1{2^{n-1}}\sum_{k=0}^{\lfloor \frac{n-1}{2} \rfloor}\binom{n}{k}(-1)^{k}\dfrac{\sin((2k-n)x)}{2k-n}+\text{(if n is even)}\binom{n}{n/2}\dfrac{(-1)^{n/2}x}{2^{n}} $. – marty cohen Nov 07 '19 at 20:03