\(\int\displaystyle\frac{x^2 + 2x - 15}{x - 3}\,dx\) is equal to (where C is a constant of integration)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(\displaystyle\frac{x^2}{2} + 5x + C\)
The numerator factorises with x − 3 as a factor:
\(x^2 + 2x - 15 = (x + 5)(x - 3)\)
So, for \(x \ne 3\),
\( \displaystyle \frac{x^2 + 2x - 15}{x - 3} = x + 5 \)
Integrating term by term:
\( \displaystyle \int (x + 5)\,dx = \frac{x^2}{2} + 5x + C \)