A) \[\log |x-\sqrt{{{x}^{2}}-1}|-{{\tan }^{-1}}x+C\]
B) \[\log |x+\sqrt{{{x}^{2}}-1}|-{{\tan }^{-1}}x+C\]
C) \[\log |x-\sqrt{{{x}^{2}}-1}|-{{\sec }^{-1}}x+C\]
D) \[\log |x+\sqrt{{{x}^{2}}-1}|-{{\sec }^{-1}}x+C\]
Correct Answer: D
Solution :
Let \[I=\int{\frac{\sqrt{x-1}}{x\sqrt{x+1}}}dx=\int{\frac{x-1}{x\sqrt{{{x}^{2}}-1}}}dx\] \[=\int{\frac{dx}{\sqrt{{{x}^{2}}-1}}-\int{\frac{dx}{x\sqrt{{{x}^{2}}-1}}}}\] \[=\log |x+\sqrt{{{x}^{2}}+1}|-{{\sec }^{-1}}x+C\]
You need to login to perform this action.
You will be redirected in
3 sec
