How do I integrate x/(x^2 + 3) ?

To solve this you need to integrate by substitution. You can spot this because the differential of the bottom of the fraction is a multiple of the top part, showing this quickly; if u = x + 3 (the bottom part) then du/dx = 2x, which is a multiple of 2 greater than x (the top part). So if we continue using u = x2 + 3 by substituting that into the equation as well as substituting the dx term (at the end of the integral) by using a rearrangement of du/dx = 2x [dx = du/2x]. Thus we are left with: Integral of (x/u).(du/2x), this means we can cancel the x terms out leaving us with (1/2). Integral 1/u.du which will equal (1/2) ln(u), so substituting out u finally gives us (1/2) ln( x2 + 3).

KM
Answered by Knox M. Maths tutor

10717 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Two masses A and B, 2kg and 4kg respectively, are connected by a light inextensible string and passed over a smooth pulley. The system is held at rest, then released. Find the acceleration of the system and hence, find the tension in the string.


Express 4x/(x^2-9)-2/(x+3) as a single fraction in its simplest form


Integrate | x^7 (ln x)^2 dx ( | used in place of sigma throughout question)


Integration question 1 - C1 2016 edexcel


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