Integral Calculus Question 479
Question: $ \int{{e^{3\log x}}{{(x^{4}+1)}^{-1}}dx} $ =
[MP PET 2001]
Options:
A) $ \log (x^{4}+1)+c $
B) $ \frac{1}{4}\log (x^{4}+1)+c $
C) $ -\log (x^{4}+1)+c $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ I=\int{{e^{3\log x}}{{(x^{4}+1)}^{-1}}dx} $ $ =\int{{e^{\log x^{3}}}{{(x^{4}+1)}^{-1}}dx} $ $ =\frac{1}{4}\int{\frac{4x^{3}}{(x^{4}+1)}dx}=\frac{1}{4}\log (x^{4}+1)+c $ .
BETA
