Integrate (x^2+4x+13)/((x+2)^2)(x-1) dx by using partial fractions

Express (x2+4x+13) / (x+2)2(x-1) as partial fractions. (x2+4x+13) / (x+2)2(x-1) = a/(x+2) +b/(x+2)2 +c/(x-1) where a, b and c are constants to be found. Multiplying by the denominator, we get (x2+4x+13) = a(x+2)(x-1) + b(x-1) + c(x+2)2 By setting x=1, we get 18=9c so c=2 By setting x=-2, we get 9=-3b so b=-3 By setting x=0 (or any other number) and using c=2 and b=-3, we get (for x=0) 13=-2a+3+8 so a=-1 Hence, (x2+4x+13) / (x+2)2(x-1) = -1/(x+2) -3/(x+2)2 + 2/(x-1) Integrating the partial fraction, we get -1ln(x+2) + (-3)(-1)(x+2)-2+1 + 2ln(x-1) +c where c is the constant of integration This simplifies down to -ln(x+2) +3/(x+2) +2ln(x-1) +c

DW
Answered by Donny W. Maths tutor

4239 Views

See similar Maths A Level tutors

Related Maths A Level answers

All answers ▸

The curve C has the equation ye ^(–2x) = 2x + y^2 . Find dy/dx in terms of x and y.


Differentiate the function f(x) = sin(x)/(x^2 +1) , giving your answer in the form of a single fraction. Is x=0 a stationary point of this curve?


How do you differentiate a^x?


Find the two real roots of the equation x^4 -5=4x^2 Give the roots in an exact form.


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