# Thread: Help with some intergration

1. ## Help with some intergration

Hello

I need help with these 3 intergrations questions please

thanks

Kind Regards

2. Originally Posted by rpatel
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 $\displaystyle \arcsin(x)=\varphi$

3. Originally Posted by Mathstud28
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.
....or you could have made the simple substitution $\displaystyle z=x-x^2$ which would convert the integral into $\displaystyle -\int z^{-\frac{1}{2}}\,dz$.

4. Originally Posted by Chris L T521
....or you could have made the simple substitution $\displaystyle z=x-x^2$ which would convert the integral into $\displaystyle -\int z^{-\frac{1}{2}}\,dz$.
....nu uh....