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

Matt E.

Degree: Molecular Biology (Doctorate) - Queen's, Belfast University

Subjects offered:Maths, Science+ 4 more

Human Biology
-Personal Statements-

“I am a first year PhD student at the School of Biological Sciences at Queen's University, Belfast, having graduated with a first class honours degree in Biology from QUB. My research focuses on the molecular mechanisms underpinning th...”

MyTutor guarantee

£20 /hr

Becky H.

Degree: Mathematics (Masters) - Exeter University

Subjects offered:Maths


“I have always loved Maths and have always found it mind-bogglingly enjoyable – this is why I’m doing a degree in Maths at Exeter University. My enthusiasm will shine through from the start and I’m told this can be really infectious! I...”

George S. GCSE Further Mathematics  tutor, A Level Further Mathematic...
£20 /hr

George S.

Degree: Physics (Masters) - Birmingham University

Subjects offered:Maths, Physics+ 2 more

Further Mathematics

“About Me: I am just entering my first year to study Physics at University of Birmingham, I've always enjoyed anything maths based hence my A-level choices, I hope I can help you through your work whether it's GCSE or A-level and maybe...”

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

What are the roots of 3x^2 + 13x + 4 ?

Find the derivative of f(x)=x^2log(2x)

What is a 'derivative'?

(Using the Quotient Rule) -> Show that the derivative of (cosx)/(sinx) is (-1)/(sinx).

View A Level Maths tutors

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