integration help needed 4 assessment (1 Viewer)

[ryanox]

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]

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???

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.

 

[Riviet]

(1+x)/(1-x) = [-(1-x)+2]/(1-x)
= -1 + 2/(1-x). Integrating this yields -x - 2ln(1-x) + C

 

[ryanox]

ok.....but how does 1+x/1-x give (-1(1-x)+2)/(1-x)???

 

[Trev]

The numerator: (-1(1-x)+2) expands to (-1+x+2) = (1+x); the original question.