My friends and I have each worked through this integral to come up with the same answer but it does not match the one from WolframAlpha and other online resources. We are trying to integrate: sqrt(5-x^2)/x dx. Using trig substitutions, I have come up with sqrt(5-x^2)-sqrt(5)lnabs((sqrt(5)+sqrt(5-x^2))/x)+C
This seems to be correct except the internet shows that the numerator of the insides of the natural log is off by a factor of sqrt(5). The trig substitution seems to be correct: csc= sqrt(5)/x, cot = sqrt(5-x^2)/x , cos =sqrt(5-x^2)/sqrt(5) Maybe my friends and I are missing a property of the natural log or maybe the internet is misleading us. Some clarity would be appreciated.
This seems to be correct except the internet shows that the numerator of the insides of the natural log is off by a factor of sqrt(5). The trig substitution seems to be correct: csc= sqrt(5)/x, cot = sqrt(5-x^2)/x , cos =sqrt(5-x^2)/sqrt(5) Maybe my friends and I are missing a property of the natural log or maybe the internet is misleading us. Some clarity would be appreciated.