R ryanox Member Joined Jun 22, 2006 Messages 62 Gender Male HSC 2006 Jun 24, 2006 #1 how do u integrate x+7/x-1 from e+1 to 2???? similarly, show that 1+x/1-x = -1 + 2/1-x and hence find the integral of 1+x/1-x dx???
how do u integrate x+7/x-1 from e+1 to 2???? similarly, show that 1+x/1-x = -1 + 2/1-x and hence find the integral of 1+x/1-x dx???
onebytwo Recession '08 Joined Apr 19, 2006 Messages 823 Location inner west Gender Male HSC 2006 Jun 24, 2006 #2 ryanox said: how do u integrate x+7/x-1 from e+1 to 2???? similarly, show that 1+x/1-x = -1 + 2/1-x and hence find the integral of 1+x/1-x dx??? Click to expand... make the top, x-1+8, then just divide, to get 1+[8/(x-1)] then integrate to get x + 8ln(x-1), then put the the numbers in same thing for the secong part. Last edited: Jun 24, 2006
ryanox said: how do u integrate x+7/x-1 from e+1 to 2???? similarly, show that 1+x/1-x = -1 + 2/1-x and hence find the integral of 1+x/1-x dx??? Click to expand... make the top, x-1+8, then just divide, to get 1+[8/(x-1)] then integrate to get x + 8ln(x-1), then put the the numbers in same thing for the secong part.
R Riviet . Joined Oct 11, 2005 Messages 5,584 Gender Undisclosed HSC N/A Jun 24, 2006 #3 (1+x)/(1-x) = [-(1-x)+2]/(1-x) = -1 + 2/(1-x). Integrating this yields -x - 2ln(1-x) + C
R ryanox Member Joined Jun 22, 2006 Messages 62 Gender Male HSC 2006 Jun 24, 2006 #4 ok.....but how does 1+x/1-x give (-1(1-x)+2)/(1-x)???
Trev stix Joined Jun 28, 2004 Messages 2,035 Location Pine Palace, St. Lucia, Brisbane. Gender Male HSC 2005 Jun 24, 2006 #5 The numerator: (-1(1-x)+2) expands to (-1+x+2) = (1+x); the original question.
