Q. $\int_{}^{}{x^{x}(1 + \log{|x|)dx}}$ is equal to
A) $x^{x}\log{|x| + c}$
B) $e^{x^{x}} + c$
C) $x^{x} + c$
D) None of these
Explanation
(c)
Put $x^{x} = t$
$\Rightarrow x^{x}(1 + \log_{e}{|x|)dx} = dt$
$\therefore\ \int_{}^{}{x^{x}(1 + {\log_{e}{|x|)dx = t + c = x}}^{x} + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.