Mathematics

# Solve : $\displaystyle \int \dfrac{x^2 + x + 5}{3x + 2} dx$

##### SOLUTION
$\dfrac{x^2+x+5}{3x+2}$

$=\dfrac{x}{3}+\dfrac{\dfrac{x}{3}+5}{3x+2}$

$=\dfrac{x}{3}+\dfrac{1}{9}+\dfrac{\dfrac{43}{9}}{3x+2}$

$\dfrac{x^2+x+5}{3x+2}=\dfrac{x}{3}+\dfrac{1}{9}+\dfrac{43}{9(3x+2)}$

$\int \dfrac{x^2+x+5}{3x+2} dx = \int \left ( \dfrac{x}{3}+\dfrac{1}{9}+\dfrac{43}{9(3x+2)}\right )dx$

$=\dfrac{x^2}{6}+\dfrac{x}{9}+\dfrac{43}{9}\left ( \dfrac{1}{3} \ln \left | 3x+2 \right |\right )+C$

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Subjective Medium Published on 17th 09, 2020
Questions 203525
Subjects 9
Chapters 126
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