MYTUTOR SUBJECT ANSWERS

151 views

Integrate (x+4)/(x^2+2x+2)

At first glance, this may look like an inverse trig integral but as the top contains an x term, we must use a different method.

First, rewrite the top in two parts, one that is a multiple of the derivative of the bottom and one that is just a number. In this case the derivative of the bottom is 2x+2 so rewrite as (2x+2)/2+3.

Now split the fraction in two: (2x+2)/2(x2+2x+2)+3/(x2+2x+2). The first part is now a log integral integrating to 1/2 ln(x2+2x+2).

To integrate the second we must complete the square on the bottom. x2+2x+2=(x+1)2+1. Now using the substitution u=x+1, dx=du, we can see that the second part is an inverse tan integral integrating to arctan(x+1).

The overall integral is therefore 1/2 ln(x2+2x+2) + arctan(x+1).

Zac T. A Level Chemistry tutor, A Level Further Mathematics  tutor, A...

5 months ago

Answered by Zac, an A Level Further Mathematics tutor with MyTutor

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

70 SUBJECT SPECIALISTS

£20 /hr

Max B.

Degree: Physics (Masters) - Exeter University

Subjects offered: Further Mathematics , Physics+ 2 more

Further Mathematics
Physics
Maths
Chemistry

“Hello! I'm studying for a masters in physics at Exeter university. I've so far achieved an overall1st in my university carrer. I'm a massive fan of everything sciency and love getting into thenitty gritty of each topic as opposed to s...”

£20 /hr

George I.

Degree: Electrical and Electronic Engineering (Masters) - Bristol University

Subjects offered: Further Mathematics , Maths

Further Mathematics
Maths

“About Me: I am currently a third year Electrical and Electronic engineering undergraduate at the University of Bristol. I have always enjoyed taking mathematics and further mathematics as I look forward to tackling problems with nume...”

MyTutor guarantee

£20 /hr

Guy P.

Degree: Mathematics (Masters) - Warwick University

Subjects offered: Further Mathematics , Maths+ 2 more

Further Mathematics
Maths
.STEP.
.MAT.

“About:Hi. I am a 2nd Year Mathematics student at the University of Warwick. I achieved a comfortable First in Year 1 and have continued this trend into my second year. Even from an early age, I have had a burning passion to engage m...”

About the author

Zac T.

Currently unavailable: until 03/10/2016

Degree: Natural Sciences (Bachelors) - Cambridge University

Subjects offered: Further Mathematics , Science+ 4 more

Further Mathematics
Science
Physics
Maths
Chemistry
Biology

“About me I am a student at the University of Cambridge where I study Natural Sciences, a course which allows me to maintain my interest in multiple areas of science and maths. I take modules in Chemistry, Physics, Earth Science and Ma...”

MyTutor guarantee

You may also like...

Posts by Zac

Find the shortest distance between the line L: x=1+t, y=1+2t, z=1-t and the point A: (2,3,4)

How can the average speedx of a gas molecule be derived?

Integrate (x+4)/(x^2+2x+2)

Why are transition metal complexes coloured?

Other A Level Further Mathematics questions

Are we able to represent linear matrix transformations with complex numbers?

What is a complex number?

What are polar coordinates?

Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

View A Level Further Mathematics tutors

Cookies:

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

mtw:mercury1:status:ok