Q. The value of $\int_{}^{}\frac{x^{2}}{1 + x^{6}}dx$ is
A) $x^{3} + c$
B) $\frac{1}{3}\tan^{- 1}{\left( x^{3} \right) + c}$
C) $\log{(1 + x^{3})}$
D) None of these
Explanation
(b)
Let $I = \int_{}^{}\frac{x^{2}}{1 + x^{6}}\ dx$
Put $x^{3} = t\ \ \Rightarrow \ x^{2}dx = \frac{1}{3}\ dt$
$\therefore\ I = \frac{1}{3}\int_{}^{}\frac{1}{1 + t^{2}}\ dt = \frac{1}{3}\tan^{- 1}{(x^{3})} + c$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.