Integral Calculus Question 354
Question: $ \int{x^{3}\log xdx=} $
[Karnataka CET 2002]
Options:
A) $ \frac{x^{4}\log x}{4}+c $
B) $ \frac{1}{16}[4x^{4}\log x-x^{4}]+c $
C) $ \frac{1}{8}[x^{4}\log x-4x^{2}]+c $
D) $ \frac{1}{16}[4x^{4}\log x+x^{4}]+c $
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int{x^{3}\log x,dx} $ $ =\frac{x^{4}}{4}\log x-\int{\frac{x^{4}}{4}\frac{1}{x}dx+c} $ $ =\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}[4x^{4}\log x-x^{4}]+c $ .
BETA
