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anonymous
 one year ago
Evaluate the definite integrals.
\[\int\limits_{0}^{4} (\frac{ 3 }{ 2x+1 })dx\]
anonymous
 one year ago
Evaluate the definite integrals. \[\int\limits_{0}^{4} (\frac{ 3 }{ 2x+1 })dx\]

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0New limit x=0, u=1 x=4, u=9

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So it would like this?.. \[\int\limits_{1}^{9}\frac{ 3 }{ u }du\] ??

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1not quite, there is a mistake with differential du=2dx dx = ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh so it would be: \[\int\limits_{1}^{9}\frac{ 3 }{ 2u }du\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then I got 3/2ln9 as the final answer..?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Is it possible to reduce that even more?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1use the log property \[\large n\,\log x ~~=~~\log x^n \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I'm not sure how to use it correctly...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \frac{3}{2}\,\ln(9) ~~=~~\ln (9^{\frac{3}{2}}) \]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Then what happens?...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.1\[\large \frac{3}{2}\,\ln(9) ~~=~~\ln (9^{\frac{3}{2}}) =\ln({\sqrt{9~}}^3)\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh I see! It would be 3ln3!
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