Question

Integral of 2v+3/3v+4 dv

Answer 1

Hope am i right

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Answer 2

Answer:

$\dfrac{2}{3}v\ +\ \dfrac{1}{3}log(3v+4)$

Step-by-step explanation:

We have to find the value of

  $\int{\dfrac{2v+3}{3v+4}dv}$

$=\int{\dfrac{\dfrac{2}{3}(3v+\dfrac{9}{2})}{3v+4}dv}$

$=\int{\dfrac{\dfrac{2}{3}(3v+4+\dfrac{1}{2})}{3v+4}dv}$

$=\int{\dfrac{2}{3}dv}\ +\ \int{\dfrac{1}{3(3v+4)}dv}$

$=\dfrac{2}{3}v+\dfrac{1}{3}log(3v+4)$

Hence, the integral of

$\int{\dfrac{2v+3}{3v+4}dv}$

can be given by

$=\dfrac{2}{3}v+\dfrac{1}{3}log(3v+4)$.