integrate 6x/(2x+1)

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integrate 6x/(2x+1)

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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\[\int\limits_{}^{}\frac{ 6x }{ 2x+1 }dx\]
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...
ah, I see... never would've gotten that lol thanks so much! :)

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yw!
BTW, although you said you'd never think of this yourself, next time you will!
haha thanks :)

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