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Question: Answered & Verified by Expert
$\int \frac{x^2+x-1}{x^2+x-6} d x=$
MathematicsIndefinite IntegrationJEE Main
Options:
  • A $x+\log (x+3)+\log (x-2)+c$
  • B $x-\log (x+3)+\log (x-2)+c$
  • C $x-\log (x+3)-\log (x-2)+c$
  • D None of these
Solution:
2314 Upvotes Verified Answer
The correct answer is: $x-\log (x+3)+\log (x-2)+c$
$\begin{aligned} & \int \frac{x^2+x-1}{x^2+x-6} d x=\int\left[1+\frac{5}{x^2+x-6}\right] d x \\ & =\int\left[1+\frac{5}{(x+3)(x-2)}\right] d x=\int d x+\int \frac{d x}{x-2}-\int \frac{d x}{x+3} \\ & =x+\log (x-2)-\log (x+3)+c\end{aligned}$

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