A) \[\frac{1}{2}{{x}^{2}}+c\]
B) \[\frac{1}{2}\sin \left[ 2{{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right]+c\]
C) \[-\frac{1}{2}{{x}^{2}}+c\]
D) \[\frac{1}{2}x+c\]
E) \[-\frac{1}{2}x+c\]
Correct Answer: C
Solution :
Let\[I=\int{\cos \left[ 2{{\cot }^{-1}}\sqrt{\frac{1-x}{1+x}} \right]}\,dx\] \[=\int{\cos [{{\cos }^{-1}}(-x)]}\,dx\] \[=-\frac{{{x}^{2}}}{2}+c\]
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