Indefinite integral of $\sin^8(x)$ Suppose we have the following function:
$$\sin^8(x)$$
We have to find its anti-derivative
To find the indefinite integral of $\sin^4(x)$, I converted everything to $\cos(2x)$ and $\cos(4x)$ and then  integrated. However this method wont be suitable to find the indefinite integral $\sin^8(x)$ since we have to expand a lot. Is there any other way I can evaluate it easily, and more efficiently?

There is well known recursion:
$$\boxed{I_n=\int\sin^nx \space dx = -\frac{1}{n}\sin^{n-1}x \cdot \cos x + \frac{n-1}{n} \cdot I_{n-2}}.$$
