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

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SUMMARY

The integral of 1/(1-x)^2 dx is not equal to x/(1-x) without the inclusion of a constant term. The correct expression for the indefinite integral is ∫ 1/(1-x)^2 dx = x/(1-x) + C, where C represents the constant of integration. This conclusion is supported by differentiating the result to verify its accuracy, as emphasized by forum contributors HallsofIvy and others. The discussion clarifies the importance of including the constant term in indefinite integrals.

PREREQUISITES
  • Understanding of indefinite integrals
  • Knowledge of differentiation techniques
  • Familiarity with calculus notation
  • Basic algebra skills
NEXT STEPS
  • Review the Fundamental Theorem of Calculus
  • Practice differentiation of various integral forms
  • Explore the concept of integration constants in indefinite integrals
  • Study advanced integration techniques, such as integration by parts
USEFUL FOR

Students studying calculus, educators teaching integration concepts, and anyone looking to solidify their understanding of indefinite integrals and differentiation.

gigi9
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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)
 
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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?
 
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?
 
My book say "SHOW THAT THE FOLLOWING INTEGRAL IS CORRECT"
 

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