Sunday

April 20, 2014

April 20, 2014

Posted by **marsha** on Wednesday, May 23, 2007 at 5:29pm.

y lny dy

i know it's integration by parts but i get confused once you have to do it the second time

Leibnitz rule (a.k.a. product rule):

d(fg) = f dg + g df

y lny dy = d[y^2/2 ln(y)] - y/2 dy

---->

Integral of y lny dy =

y^2/2 ln(y) - y^2/4 + const.

Instead of partial integration you can use this trick:

Integral of y^a dy = y^(a+1)/(a+1) (1)

Differentiate both sides w.r.t. a:

Integral of y^a Ln(y) dy =

y^(a+1)Ln(y)/(a+1) -y^(a+1)/(a+1)^2 (2)

uUp to an integration constant)

Substitute a = 1 to obtain the answer. Note that the integration constant we could have added to (1) can still depend on the parameter a. So, if you differentiate it you get an integration constant in (2)

**Related Questions**

calc - also: integral of tan^(-1)y dy how is integration of parts used in that? ...

math - evaluate the double integral and reverse order of integration [(first ...

brief calc - evaluate the integral using integration by parts 7xe^-x

integration by parts - s- integral s ln (2x+1)dx ? = ln(2x+1)x - s x d( ln (2x+1...

Calc - Use integration by parts to evaluate the integral. ∫ from 1 to 4 of...

Stats: Joint Density Function - Let the joint density function of X and Ybe ...

Calculus II - Evaluate the integral using method of integration by parts: (...

Calc - evaluate the indefinite integral: x^13(cos(x^7))dx I've tried using ...

improper integral - can any one explain how to evaluate this improper integral i...

calculus - 8). Part 1 of 2: In the solid the base is a circle x^2+y^2=16 and the...