Q. $\int_{}^{}\frac{dx}{x^{2} + 4x + 13}$ is equal to
A) $\log{\left( x^{2} + 4x + 13 \right) + c}$
B) $\frac{1}{3}\tan^{- 1}{\left( \frac{x + 2}{3} \right) + c}$
C) $\log{(2x + 4) + c}$
D) $\frac{2x + 4}{\left( x^{2} + 4x + 13 \right)^{2}} + c$
Explanation
(b)
$\int_{}^{}\frac{dx}{x^{2} + 4x + 13} = \int_{}^{}\frac{dx}{x^{2} + 4x + 4 + 9}$
$= \int_{}^{}\frac{dx}{(x + 2)^{2} + 3^{2}} = \frac{1}{3}\tan^{- 1}{\left( \frac{x + 2}{3} \right) + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.