Question

integrate 6x/(2x+1)

Answer 1

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

Answer 2

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...

Answer 3

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

Answer 4

yw!

Answer 5

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

Answer 6

haha thanks :)