Integrating Rational Functions: Is It Possible?

[Oblivionator]

Evaluate the integral:

int ((x+1)/(x-1)) dx

is this possible?

i tried searching for this but there was no answer

 

[lurflurf]

(x+1)/(x-1)=[(x-1)+2]/(x-1)=1+2/(x-1)

Have you ever seen a function g such that g'=f'/f
?

 

[Oblivionator]

(x+1)/(x-1)=[(x-1)+2]/(x-1)=1+2/(x-1)

could you please explain this?

im having problems integrating ((x+1)/(x-1)) dx

 

[Oblivionator]

no wait, could you please fully solve the problem?

 

[HallsofIvy]

(x+1)/(x-1)=[(x-1)+2]/(x-1)=1+2/(x-1)

could you please explain this?

im having problems integrating ((x+1)/(x-1)) dx

If you cannot do basic algebra you are going to have great difficulty integrating any function. The above is just simple division. And you can see it is true just by adding the fractions on the right hand side.

no wait, could you please fully solve the problem?

It would be much better for you to try yourself. Do you know the anti-derivative of 1/x?

 

[Oblivionator]

no, not yet but thank you

 

[HallsofIvy]

Then why in the world are you trying to do this problem?

 

[Oblivionator]

Sorry, I just like to read ahead in my textbook

 

[HallsofIvy]

Good! Just don't be upset if you are often puzzled!