Integral Calculus Question 411
Question: $ \int_{{}}^{{}}{\frac{x}{1+x^{4}}\ dx=} $
[IIT 1978; UPSEAT 2002]
Options:
A) $ \frac{1}{2}{{\cot }^{-1}}x^{2}+c $
B) $ \frac{1}{2}{{\tan }^{-1}}x^{2}+c $
C) $ {{\cot }^{-1}}x^{2}+c $
D) $ {{\tan }^{-1}}x^{2}+c $
Show Answer
Answer:
Correct Answer: B
Solution:
Put $ t=x^{2}\Rightarrow dt=2x,dx, $ therefore $ \int_{{}}^{{}}{\frac{x}{1+x^{4}},dx=\frac{1}{2}\int_{{}}^{{}}{\frac{1}{1+t^{2}},dt=\frac{1}{2}{{\tan }^{-1}}t+c=\frac{1}{2}{{\tan }^{-1}}x^{2}+c}} $ .
BETA
