# Evaluate the following integrals. int_0^3frac{2x-1}{x+1}

Evaluate the following integrals.
${\int }_{0}^{3}\frac{2x-1}{x+1}$
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Mayme
$\text{Consider the given integral}$
${\int }_{0}^{3}\frac{2x-1}{x+1}$

$\text{So, the integral becomes:}$
${\int }_{1}^{4}\frac{2\left(u-1\right)-1}{u}du$
$⇒{\int }_{1}^{4}\frac{2u-3}{u}du$
$⇒{\int }_{1}^{4}\frac{2u}{u}-\frac{3}{u}du$
$⇒{\int }_{1}^{4}2-\frac{3}{u}du$
$=2u-3\mathrm{ln}\left(u\right){|}_{1}^{4}$
$=2\left(4\right)-3\mathrm{ln}\left(4\right)-2\left(1\right)+3\mathrm{ln}\left(1\right)$
$⇒8-3\mathrm{ln}\left(4\right)-2+3\left(0\right)$
$⇒6-3\mathrm{ln}\left({2}^{2}\right)$
$⇒6-6\mathrm{ln}\left(2\right)$