Integral Calculus Question 210
Question: $ \int{{e^{3\log x}}{{(x^{4}+1)}^{-1}}dx} $ is equal to
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:
[b] $ \int{{e^{3\log x}}{{(x^{4}+1)}^{-1}}dx=\int{{e^{\log x^{3}}}\frac{1}{x^{4}+1}dx}} $ $ =\int{\frac{x^{3}}{x^{4}+1}dx=\frac{1}{4}\log (x^{4}+1)+C} $ [since $ {e^{\log x^{3}}}=x^{3} $ ]
BETA
