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
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