How does integration by parts work ad when to use it?

Integration by parts should be used when you want to integrate a function composed of two factors (we can call them 'u' and 'dv'), where it is fairly easy to derive 'u', while it is difficult or impossible to do it with 'dv'. For instance f(x)=xln(x) should be integrated by parts following 4 steps:Decide which factor is your 'u'. To do this you can almost always use an acronym 'LIATE'. Whichever function of the following: logarithmic, inverse trig., algebraic, trig., exponential, comes first is your 'u'. In our case 'u' = ln(x) as it is a logarithmic function and dv= x dxDerive 'u' to find 'du'. Integrate 'dv' to find 'v'.Apply the formula Integral [(vdv) dx] = uv- integral[(vdu) dx]Solve for the boundaries or add a constant 'c' if these were undefined.I will use the whiteboard to solve the example for you, please stop me and ask if I am going too fast. After this, I will give you some functions to practice with. I want to make sure if you have a good understanding of this topic.

MO
Answered by Michal O. Maths tutor

2984 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is greater e^pi or pi^e?


The equation of a circle is x^2-6x+y^2+4y=12. Complete the square to find the centre and radius of the circle.


find dy/dx for the equation y = 6x ^(1/2)+x+3


Can you explain the sum of 1 to 100?


We're here to help

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

MyTutor is part of the IXL family of brands:

© 2025 by IXL Learning