A) \[\frac{x}{2}\sqrt{1+{{x}^{2}}}+\frac{1}{2}\log (x+\sqrt{1+{{x}^{2}}})+c\]
B) \[\frac{2}{3}{{(1+{{x}^{2}})}^{3/2}}+c\]
C) \[\frac{2}{3}x{{(1+{{x}^{2}})}^{3/2}}+c\]
D) None of these
Correct Answer: A
Solution :
\[\int_{{}}^{{}}{\sqrt{1+{{x}^{2}}}}dx=\frac{x}{2}\sqrt{{{x}^{2}}+1}+\frac{1}{2}\log (x+\sqrt{{{x}^{2}}+1})+c\].
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