Mathematics

Solve
$$I= \displaystyle\int \dfrac{x+2}{x^{2}+5x+6}dx$$


SOLUTION
We have,
$$I=\displaystyle \int\dfrac{x+2}{x^2+5x+6}dx$$
$$I=\displaystyle \int\dfrac{x+2}{x^2+3x+2x+6}dx$$
$$I=\displaystyle \int\dfrac{x+2}{(x+3)(x+2)}dx$$
$$I=\displaystyle \int\dfrac{1}{(x+3)}dx$$
on Integrating and we get,
$$I=\log(x+3)+c \ \ \because \displaystyle \int \dfrac{1}{x}dx=\log2$$
Hence, this is the answer.
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Subjective Medium Published on 17th 09, 2020
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