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

3896 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

What is a derivative?


Solve the equation: 2x+3y=8 & 3x-y=23


Find the stationary point of y=3x^2-12x+29 and classify it as a maximum/minimum


The graph above shows the line y = 3*x^2. Find the area beneath the graph from y = 0 to y = 5.


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