1. ## Integral. #4

hellloo
I posted these problems for fun
you can post full solutions
its not for my homework
I did not post them in the challenge problem sub-forum because i do not know the solutions .. also because am not ready to PM 20 persons

heeeereeee is ittttt:
Evaluate:

$\displaystyle \int \frac{dx}{\sqrt{-2x^2+3x+4}}$

2. Originally Posted by TWiX
hellloo
I posted these problems for fun
you can post full solutions
its not for my homework
I did not post them in the challenge problem sub-forum because i do not know the solutions .. also because am not ready to PM 20 persons

heeeereeee is ittttt:
Evaluate:

$\displaystyle \int \frac{dx}{\sqrt{-2x^2+3x+4}}$
$\displaystyle -2x^2+3x+4=-2(x^2 - \frac{3}{2}x-2)=-2 \left( \left(x - \frac{3}{4}\right)^2-\left( \frac{\sqrt{41}}{4} \right)^2 \right)$
$\displaystyle =2\left( \left( \frac{\sqrt{41}}{4} \right)^2 - \left(x - \frac{3}{4}\right)^2 \right)$

So the integral will be : $\displaystyle \frac{1}{\sqrt{2}} \int \frac{dx}{\sqrt{ \left( \frac{\sqrt{41}}{4} \right)^2 - \left(x - \frac{3}{4}\right)^2 }}$
$\displaystyle =\frac{1}{\sqrt{2}} sin^{-1}\left( \frac{4x-3}{\sqrt{41}} \right) + C$