Q. $\int_{}^{}\frac{4^{x + 1} - 7^{x - 1}}{28^{x}}\ dx$ is equal to
A) $\frac{1}{7\ \log_{e}4}4^{- x} - \frac{4}{\log_{e}7}7^{- x} + c$
B) $\frac{1}{7\ \log_{e}4}4^{- x} + \frac{4}{\log_{e}7}7^{- x} + c$
C) $\frac{4^{- x}}{\log_{e}7} - \frac{7^{- x}}{\log_{e}4} + c$
D) $\frac{4^{- x}}{\log_{e}4} - \frac{7^{- x}}{\log_{e}7} + c$
Explanation
(a)
Let $I = \int_{}^{}\frac{4^{x + 1} - 7^{x - 1}}{28^{x}}\ dx$
$= 4\int_{}^{}\frac{1}{7^{x}}\ dx - \frac{1}{7}\ \int_{}^{}\frac{1}{4^{x}}\ dx = - \frac{4.7^{- x}}{\log_{e}7} + \frac{1}{7\ \log_{e}4}4^{- x} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.