While I was doing integration. I got an example which looks like,
$$\int \frac{(\sin^{-1}x)^2}{\sqrt{1-x^2}}dx$$
I just took $\sin^{-1}x=z$. At the last moment of integration. I got an equation something just like this (Here most of people are very professional that's why I am not writing all steps cause, the question will become very big).
$$\int z^2 dz$$ $$=\frac{z^3}{3}+c$$ $$=\frac{(\sin^{-1}x)^3}{3}+c$$
In my book, they have written. $$\frac{z^3}{3}+c=\frac{1}{3}\cdot (\sin^{-1}x)^2+c$$
I guess power of $\sin^{-1}x$ should cube.
