Integrate, by parts, y=xln(x),

First, we need to separate the RHS as components of U and V. Using the LATE (logarithms, algebra, trigonometry, exponentials) technique, we see that logarithms have priority to algebra hence U = lnx and dV/dx = x. Next, we differentiate the U and integrate the dV/dx to obtain dU/dx = 1/x and V = x2/2. To integrate by parts we do: UV minus the integral of dU/dx times V. Thus, I (the integral) = (x2/2)lnx - ∫x/2.dx and once integrated the integral becomes (x2/2)lnx - x2/4 + C (never forget the constant C for the general solution to an integration problem).

MS
Answered by Makhdoom S. Maths tutor

3125 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is a logarithm?


Fnd ∫x^2e^x


The mass, m grams, of a substance is increasing exponentially so that the mass at time t hours is m=250e^(0.021t). Find the time taken for the mass to double in value.


The complex numbers Z and W are given by Z=3+3i and W=6-i. Giving your answers in the form of x+yi and showing how you clearly obtain them, find: i) 3Z-4W ii) Z*/W


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences