Hello
I need help with these 3 intergrations questions please
thanks
Kind Regards
1. $\displaystyle \begin{aligned}\frac{2x-1}{\sqrt{x-x^2}}&=\frac{2x-1}{\sqrt{\frac{1}{4}(1-(1-4x+4x^2))}}\\
&=\frac{2x-1}{\sqrt{\tfrac{1}{4}(1-(1-2x)^2}}\\
&=\frac{2x-1}{\tfrac{1}{2}\sqrt{1-(1-2x)^2}}\\
&=2\frac{2x-1}{\sqrt{1-(2x-1)^2}}\end{aligned}$
Now just let $\displaystyle \varphi=2x-1$ and see the next problem.
2. $\displaystyle \int\frac{dx}{\sqrt{1-x^2}}$
Let $\displaystyle \sin(\theta)=x$
3. $\displaystyle \int\arcsin(x)dx$
Let $\displaystyle \arcsin(x)=\varphi$