Find the integral of (x+4)/x(2-x) .dx

In order to integrate the expression we must first rewrite it in terms of Partial Fractions i.e. A/x and B/(2-x), so that when multiplied together we have a fraction with same denominator as the expression we want to integrate. The numerator is then A(2-x)+B(x). We compare this to (x+4) and determine our values for A and B by equating the coefficients. 2A=4 therefore A=2. -A+B=1 therefor B=3. We now have a new integrand which is easier to solve, 2/x + 3/(2-x). Using our standard examples of integrals we see that the solution is 2ln|x|-3ln|2-x|. Be careful of the -x in 3/(2-x) as this affects the sign of ln when we integrate.

AT
Answered by Aaron T. Maths tutor

3666 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

Integrating cos^2(x)+5sin^2(x)


How should I go about solving a quadratic equation?


I don't understand the point of differentiation or integration


What is exactly differentiation?


We're here to help

contact us iconContact usWhatsapp logoMessage us on Whatsapptelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences