anonymous 3 years ago integrate 6x/(2x+1)

1. anonymous

$\int\limits_{}^{}\frac{ 6x }{ 2x+1 }dx$

2. anonymous

Try to rewrite the fraction: in the denominator, there is 2x+1. If you had that in the numerator as well, things would become easier. So, if it was: (6x+3)/(2x+1), this would be 3(2x+1)/(2x+1)=3. We cannot make it that simple, but we can go in the same direction:$\int\limits_{}^{}\frac{ 6x }{ 2x+1 }dx=\int\limits_{}^{}\frac{ 6x+3-3 }{ 2x+1 }dx=\int\limits_{}^{}\frac{ 3(2x+1)-3 }{ 2x+1 }dx$Now we can split it up:$=\int\limits_{}^{}3dx-\int\limits_{}^{}\frac{ 3 }{ 2x+1 }dx$Maybe you can try this yourself...

3. anonymous

ah, I see... never would've gotten that lol thanks so much! :)

4. anonymous

yw!

5. anonymous

BTW, although you said you'd never think of this yourself, next time you will!

6. anonymous

haha thanks :)