Integral Calculus Question 214
Question: $ \int_{{}}^{{}}{\frac{x^{3}-x-2}{(1-x^{2})}\ dx=} $
[AI CBSE 1985]
Options:
A) $ \log ( \frac{x+1}{x-1} )-\frac{x^{2}}{2}+c $
B) $ \log ( \frac{x-1}{x+1} )+\frac{x^{2}}{2}+c $
C) $ \log ( \frac{x+1}{x-1} )+\frac{x^{2}}{2}+c $
D) $ \log ( \frac{x-1}{x+1} )-\frac{x^{2}}{2}+c $
Show Answer
Answer:
Correct Answer: D
Solution:
$ \int_{{}}^{{}}{\frac{x^{3}-x-2}{(1-x^{2})},dx}=\int_{{}}^{{}}{\frac{-x(1-x^{2})}{(1-x^{2})},dx-\int_{{}}^{{}}{\frac{2}{1-x^{2}},dx}} $ $ =-\int_{{}}^{{}}{x,dx}-2\int_{{}}^{{}}{\frac{1}{1-x^{2}},dx=\frac{-x^{2}}{2}+\log ( \frac{x-1}{x+1} )+c.} $
BETA
