Q. If $\int_{}^{}\frac{x + 2}{2x^{2} + 6x + 5}\ dx = P\int_{}^{}{\frac{4x + 6}{2x^{2} + 6x + 5}\ dx} + \frac{1}{2}\int_{}^{}\frac{dx}{2x^{2} + 6x + 5}$ , then the value of $P$ is
A) $\frac{1}{3}$
B) $\frac{1}{2}$
C) $\frac{1}{4}$
D) 2
Explanation
(c)
$\int_{}^{}\frac{x + 2}{2x^{2} + 6x + 5}\ dx = \frac{1}{4}\int_{}^{}\frac{4x + 6 + 2}{2x^{2} + 6x + 5}\ dx$
$= \frac{1}{4}\ \int_{}^{}\frac{4x + 6}{2x^{2} + 6x + 5}\ dx + \frac{1}{2}\int_{}^{}\frac{dx}{2x^{2} + 6x + 5}\$
$\Rightarrow \ P = \frac{1}{4}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.