How would you prove the 'integration by parts' rule?

This involves thinking about a well-known formula (the product rule) in a slightly different way. Looking at the product rule, for two functions u and v, (uv)' = uv' + vu'. We can rewrite this as uv' = (uv)' - vu'. Integrating both sides, we obtain integral of uv' = uv - integral of vu'.

ER
Answered by Ethan R. STEP tutor

1715 Views

See similar STEP University tutors

Related STEP University answers

All answers ▸

How can I integrate e^x sin(x)?


Let y=arcsin(x)/sqrt(1-x^2). Show that (1-x^2) y'-xy-1=0, and prove that, for all integers n>=0, (1-x^2)y^{n+2}-(2n+3)xy^{n+1} -(n+1)^2 y^{n}=0. (Superscripts denote repeated differentiation)


STEP 2 - 2018, Q6i): Find all pairs of positive integers (n, p), where p is a prime number, that satisfy n! + 5 = p .


By use of calculus, show that x − ln(1 + x) is positive for all positive 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