Q85 / 150 · MHT CET 2026 (11 April Shift 1) · Mathematics
$\int \dfrac{x}{x + 2} dx$ is equal to
- A$x + 2\log(x + 2) + c$
- B$x + \log(x + 2) + c$
- C$x - \log(x + 2) + c$
- Correct answerD$x - 2\log(x + 2) + c$
Solution
Let $I = \int \dfrac{x}{x + 2} dx$
Adding and subtracting $2$ in the numerator, we get:
$I = \int \dfrac{x + 2 - 2}{x + 2} dx$
$I = \int \left(1 - \dfrac{2}{x + 2}\right) dx$
Integrating with respect to $x$:
$I = x - 2\log(x + 2) + c$
Answer: $x - 2\log(x + 2) + c$
Adding and subtracting $2$ in the numerator, we get:
$I = \int \dfrac{x + 2 - 2}{x + 2} dx$
$I = \int \left(1 - \dfrac{2}{x + 2}\right) dx$
Integrating with respect to $x$:
$I = x - 2\log(x + 2) + c$
Answer: $x - 2\log(x + 2) + c$
Hence, the correct answer is option: 'D'.