Friday

January 30, 2015

January 30, 2015

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)

**Answer this Question**

**Related Questions**

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

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

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

calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...

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

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

Please help with Calc! - Evaluate the indefinite integral. integral 2e^(2x)sin(e...

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

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

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