Mathematics

$$\int \dfrac { x ^ { 2 } + x - 1 } { x ^ { 2 } + x - 6 } d x =$$


ANSWER

$$x - \log | x + 3 | + \log | x - 2 | + c$$


SOLUTION
$$\displaystyle \int \frac{x^{2}+x-1}{x^{2}+x-6}dx=?$$

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

$$\displaystyle =\int (1+\frac{5}{(x+3)(x-2)})dx$$

$$\displaystyle =\int 1dx+\frac{5}{5}\int [\frac{1}{x-2}-\frac{1}{x+3}]dx$$

$$=x+log(x-2)-log(x+3)+c$$

$$=x-log(x+3)+log(x-2)+c$$

Option (b)
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Single Correct Medium Published on 17th 09, 2020
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