A) \[\frac{1}{2}(x-4)\sqrt{{{x}^{2}}-8x+7}+9\log [x-4+\sqrt{{{x}^{2}}-8x+7}]+c\]
B) \[\frac{1}{2}(x-4)\sqrt{{{x}^{2}}-8x+7}-3\sqrt{2}\log [x-4+\sqrt{{{x}^{2}}-8x+7}]+c\]
C) \[\frac{1}{2}(x-4)\sqrt{{{x}^{2}}-8x+7}-\frac{9}{2}\log [x-4+\sqrt{{{x}^{2}}-8x+7}]+c\]
D) None of these
Correct Answer: C
Solution :
\[\int_{{}}^{{}}{\sqrt{{{x}^{2}}-8x+7}\,dx=\int_{{}}^{{}}{\sqrt{{{(x-4)}^{2}}-{{(3)}^{2}}}\,dx}}\] Now apply formula of \[\int_{{}}^{{}}{\sqrt{{{x}^{2}}-{{a}^{2}}}\,dx.}\]
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