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