math.com
Home    |    Teacher    |    Parents    |    Glossary    |    About Us
Homework Help Practice Ask An Expert Calculators & Tools Games Store
Email this page to a friend Email this page to a friend
Resources
· Cool Tools
· Formulas & Tables
· References
· Test Preparation
· Study Tips
· Wonders of Math
 
Search
Custom Search



Math Jobs


  
Proof: Integral ln(x)
(Math | Calculus | Integrals | Table Of | ln x)
 
Discussion of
(integral) ln(x) dx = x ln(x) - x + C.

1. Proof

    Strategy: Use Integration by Parts.

    (integral)ln(x) dx

    set
      u = ln(x),    dv = dx
    then we find
      du = (1/x) dx,    v = x

    substitute

    (integral) ln(x) dx = (integral) u dv

    and use integration by parts

    = uv - (integral) v du

    substitute u=ln(x), v=x, and du=(1/x)dx

    = ln(x) x - (integral) x (1/x) dx
    = ln(x) x - (integral) dx
    = ln(x) x - x + C
    = x ln(x) - x + C.
    Q.E.D.

  
 
  

 
Contact us | Advertising & Sponsorship | Partnership | Link to us

© 2000-2005 Math.com. All rights reserved.     Legal Notices.     Please read our Privacy Policy.