Q. $\int_{}^{}\frac{dx}{x(x + 1)}\$ equals Where $c$ is an arbitrary constant
A) $\log\left| \frac{x + 1}{x} \right| + c$
B) $\log\left| \frac{x}{x + 1} \right| + c$
C) $\log\left| \frac{x - 1}{x} \right| + c$
D) $\log\left| \frac{x - 1}{x + 1} \right| + c$
Explanation
(b)
$\int_{}^{}\frac{dx}{x(x + 1)} = \int_{}^{}\frac{1}{x}dx - \int_{}^{}\frac{1}{x + 1}dx$
$= \log x - \log{(x + 1)} + c$
$= \log\left| \frac{x}{x + 1} \right| + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.