Using partial fractions, find f(x) if f'(x)=5/(2x-1)(x-3)

First step: partial fractions 5/(2x-1)(x-3) 5=A(x-3)+B(2x-1) A=0 when x=3, so B=5/(2x3-1)=1 B=0 when x=1/2, so A=5/(0.5-3)=-2 So f'(x)=1/(x-3)-2/(2x-1) Second step: Integration f(x)= (integral)(1/(x-3))dx - 2(integral)(1/(2x-1))dx = ln|x-3| - 2/2ln|2x-1| + C = ln|(x-3)/(2x-1)| + C

JF
Answered by Jasmin F. Maths tutor

4578 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

integrate 6x^2


The equation (t – 1)x^2 + 4x + (t – 5) = 0, where t is a constant has no real roots. Show that t satisfies t2–6t+1>0


I know how to integrate, but I still never see any real world example of it, so it is difficult to understand. Why is it useful?


Of the following 4 equations, 3 of them represent parallel lines. Which is the odd one out?


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