Calculus Problem: Find Integral of 1/(1-x)^2 dx

[gigi9]

Calculus help please!

Plz help me do the problem below. thanks a lot.
Show that the following integral is CORRECT:
Indefinite Integral of 1/(1-x)^2 dx = x/(1-x)

 

[HallsofIvy]

I'm afraid no one will be able to "Show that the following integral is CORRECT: Indefinite Integral of 1/(1-x)^2 dx = x/(1-x)"

because it isn't.

Did you even try differentiating to see if it was correct?

 

[Hurkyl]

As HallsofIvy stated in his post, and I stated when you asked the similar question at https://www.physicsforums.com/showthread.php?threadid=6977 , the simplest way to prove an indefinte integral correct is to differentiate.


Incidentally, whenever you're doing an indefinite integral, you have to include a constant term; so if this integral is correct, you should write

∫ 1/(1-x)^2 dx = x/(1-x) + C

(for the record, once you add the "+ C", the answer is correct)


Incidentally, gigi9, how did you come to ask us this question? Does your book say "prove this integral is correct", or did it ask you to find the integral and you derived the RHS on your own?

 

[gigi9]

My book say "SHOW THAT THE FOLLOWING INTEGRAL IS CORRECT"