Find ∫ x^2(ln(4x))dx

 ∫xln(4x)dx

Firstly , identify this question as integration by parts. Therefore set one half as value 'u' and one as value 'dv'.

Here we will set u = ln(4x).

Therefore: du/dx = 1/4x . (4)        

                       du = 1/x dx                 We then set dv = x2 dx                                                          

                                                                          dv/dx = x2                                                              

                                                                                v = x3/3

The formula for integration by parts is :

u.v -  ∫v.du

= ln(4x).(x3) -  ∫(x3/3)(1/x)dx

= x3ln(4x) - ∫(x2/3)dx

= x3ln(4x) - x3/9 + c

SF
Answered by Sally F. Maths tutor

10696 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The region below the curve y = e^x + e^(-x) and the lines x = 0, x = ln4 is rotated 2π radians about the x-axis. Find the volume of the resulting solid.


Solve, giving your answer to 3 s.f. : 2^(2x) - 6(2^(x) ) + 5 = 0


The curve C has equation y=3x^3-11x+1/2. The point P has coordinates (1, 3) and lies on C . Find the equation of the tangent to C at P.


How can I differentiate x^2+2y=y^2+4 with respect to x?


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