How you did it? Because, my dx= $$-\frac{2*\sqrt{x+2}*\left ( x+1 \right )^{2}}{\sqrt{x+1}} dt$$

Is it clear now?

but how this will help me to continue? Nothing will cancel out, should I use now partial fractions?

Yes your integral is rational now, use partial fractions, should i do it for you?

I want to try it on my own. Would you be so kind and check it then?

Yes try it and i will check it, good luck,Shelley!

First I got $$-\int\frac{4+2t^{2}}{\left ( t^{2}-3 \right )\left ( t^{2}-1 \right )} $$ and when I did partial fractions I got $$-\int \frac{5}{t^{2}-3}dt$$ and $$ \int \frac{3}{t^{2}-1}dt$$. Is it correct?

One moment plese.

I got $$\int\frac{-2(t^2+2)}{(t^2+3)(t^2+1)}dt$$

But this is the same as mine, or?

No, i have a plus sign instead of your minus sign in the denominator

$$-2(t^{2}+2)=-2t^{2}-4=-(2t^{2}+4)$$ and I put - in front of the integral

Yes this is correct, your denominator is wrong ,it must be $$(t^2+3)(t^2+1)$$

Okay, I understand the mistake now, thanks a lot

I hope your problem is solved now, should i give you the result?

yes, it would be useful

$$\int \frac{-2(t^2+2)}{(t^2+3)(t^2+1)}dt=-\arctan \left( t \right) -1/3\,\sqrt {3}\arctan \left( 1/3\,t\sqrt {3 } \right) +C$$

It really helps me, thanks a lot

I wish you a nice evening without all these integrals!

:D thanks, you too..