Q. The value of $\int_{}^{}\frac{(x + 1)^{2}}{x(x^{2} + 1)}\ dx$ is equal to
A) $\log_{e}{x + c}$
B) $\log_{e}{x + 2\tan^{- 1}{x + c}}$
C) $\log_{e}{\left( \frac{1}{x^{2} + 1} \right) + c}$
D) None of these
Explanation
(b)
Let $I = \int_{}^{}\frac{(x + 1)^{2}}{x(x^{2} + 1)}\ dx$ =$\int_{}^{}\frac{x^{2} + 1 + 2x}{x(x^{2} + 1)}\ dx$
$= \int_{}^{}\frac{1}{x}dx + \int_{}^{}\frac{2}{x^{2} + 1}dx$
$\Rightarrow \ I = \log_{e}{x + 2\tan^{- 1}{x + c}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.