Q. $\int_{}^{}{x^{3}\log{x\ dx}}$ is equal to
A) $\frac{x^{4}\log x}{4} + c$
B) $\frac{1}{16}\lbrack 4x^{4}\log{x - x^{4}\rbrack + c}$
C) $\frac{1}{8}\lbrack x^{4}\log{x - 4x^{2}\rbrack + c}$
D) $\frac{1}{16}\lbrack 4x^{4}\log{x + x^{4}\rbrack + c}$
Explanation
(b)
$\int_{}^{}{x^{3}\log{x\ dx}}$
$= \frac{x^{4}}{4}\log{x - \int_{}^{}{\frac{x^{4}}{4} \bullet \frac{1}{x}dx}}$
$= \frac{x^{4}}{4}\log{x - \int_{}^{}{\frac{x^{3}}{4}dx = \frac{x^{4}}{4}\log{x - \frac{x^{4}}{16} + c}}}$
$= \frac{1}{16}\lbrack 4x^{4}\log{x - x^{4}\ \rbrack + c}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.