Mathematics

Integrate: $$\dfrac { 3 x - 1 } { ( x + 2 ) ^ { 2 } }$$


SOLUTION
$$ I =\displaystyle \int \dfrac{3x-1}{(x+2)^{2}}dx$$

$$ u = x+2 \Rightarrow x = u-2 \Rightarrow dx = du$$

$$ I = \displaystyle\int \dfrac{3(u-2)-1}{u^{2}}du$$

$$I =\displaystyle \int \dfrac{3u-7}{u^{2}}du = \int \left(\dfrac{3}{u}-\dfrac{7}{u^{2}}\right)du$$

$$I = 3 \ln u+\dfrac{7}{u}+c$$

$$I = 3 \ln \left | x+2 \right |+\dfrac{7}{x+2}+c$$
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Subjective Medium Published on 17th 09, 2020
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