Given that (2x + 11 )/(2x + 1)(x + 3) ≡ A /(2x + 1) + B /(x + 3) , find the values of the constants A and B. Hence show that the integral from 0 to 2 (2x + 11)/ (2x + 1)(x + 3) dx = ln 15.

First starting from the right hand side.

 A /(2x + 1) + B /(x + 3) = A(x+3)+B(2x+1)/(x+3)(2x+1)

Therefore the numerator = (A+2B)x+(3A+B)

Equating this numorator with the Left hand side we are presented with the two simultaneous equations A+2B=2, 3A+B=11 yielding solutions of B=-1, A=4 by elimination of A

 Hence the integral from 0 to 2  (2x + 11)/ (2x + 1)(x + 3) dx =  integral from 0 to 2 of 4/(2x+1) - 1/(x+3) dx

=[2ln(2x+1) - ln(x+3)] from 0 to 2

= [(2ln5-ln5)-(2ln1-ln3)]



George D. A Level Further Mathematics  tutor, A Level Maths tutor, A ...

1 year ago

Answered by George, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist


£20 /hr

Jose Ignacio M.

Degree: Electronics and Software Engineering (Masters) - Edinburgh University

Subjects offered: Maths, Spanish+ 2 more


“About Me: I am a Spanish engineering student at The University of Edinburgh. Half way through my first year for an MEng degree on Electronics and Software Engineering. If you take a quick look at my grades you may think I have always ...”

MyTutor guarantee

£20 /hr

Thomas P.

Degree: Masters in Mathematics (Masters) - Oxford, Oriel College University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About Me: I am a Maths student at Oxford University. Whilst I love learning about, talking about, and generally engaging with Mathematics, that's not all I do! Outside of studying I enjoy board games, and I play squash for the Univers...”

£20 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“About Me: I am current studying a PGCE at Leeds University and should be a fully qualified teacher by the end of June 2017. I also studied maths at Leeds where I got my degree. I have always had a passion for maths and my objective is...”

About the author

George D.

Currently unavailable: until 30/06/2016

Degree: Mathematics (Masters) - Oxford, Exeter College University

Subjects offered: Maths, Physics+ 2 more

Further Mathematics

“About meI'm a first year Mathematics student at Exeter College, Oxford. I have always been enthusiastic about teaching and have experience tutoring young people of all ages in the past, from 11+ tutoring for primary school children...”

You may also like...

Other A Level Maths questions

Find the gradient of a curve whose parametric equations are x=t^2/2+1 and y=t/4-1 when t=2

What is exactly differentiation?

Where does the geometric series formula come from?

The points P (2,3.6) and Q(2.2,2.4) lie on the curve y=f(x) . Use P and Q to estimate the gradient of the curve at the point where x=2 .

View A Level Maths tutors


We use cookies to improve our service. By continuing to use this website, we'll assume that you're OK with this. Dismiss