MYTUTOR SUBJECT ANSWERS

488 views

How do you integrate e^x cos x

∫ excos x dx 

First of all, we have to think of which method we want to use to approach this problem. There are a few options we can consider such as integration by parts and substitution. In this case, integration by parts would be suitable.

Now we have to recall the integration by parts formula which is

∫ u dv/dx dx = uv - ∫ v du/dx dx
From the problem above, 
we can set u= cos x and dv/dx = ex  

du/dx = -sin x and v= ex

∫ excosx dx = excos x - ∫ ex (-sin x) dx
                   = excos x + ∫ exsinx dx

Now we have to repeat the integration by parts process again for ∫ ex sin x dx
Let u= sin x and dv/dx = ex

       du/dx = cos x and v= ex

 ∫ ex cos x dx = excos x + ( ex sin x - ∫ ex cos x dx )

2 ∫excos x dx = ecos x + esin x
∫  ex cos x dx = 1/2 ( excos x + ex sin x ) 

Ta J. A Level Chemistry tutor, A Level Maths tutor, A Level Further M...

1 year ago

Answered by Ta, an A Level Maths tutor with MyTutor


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

296 SUBJECT SPECIALISTS

£20 /hr

Matthew H.

Degree: Physics (Masters) - Liverpool University

Subjects offered:Maths, Physics+ 3 more

Maths
Physics
History
Chemistry
-Personal Statements-

“About Me  I am studying physics at the University of Liverpool and am now in my second year having passed with a first in all my modules last year. I really love all things science and have a real drive to pass on what I know to other...”

£26 /hr

Elizabeth G.

Degree: Mathematics (G100) (Bachelors) - Durham University

Subjects offered:Maths, Science+ 2 more

Maths
Science
Physics
Chemistry

“ Hello, my name is Elizabeth, I am studying maths at Durham. I love maths but also studied chemsitry and physcis at A-level. I have two younger sisters who I have helped through similar exams and have tutored various other subjects giv...”

Nick B. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor
£20 /hr

Nick B.

Degree: Computer Science (Masters) - Bristol University

Subjects offered:Maths, Physics

Maths
Physics

“About me: I am currently studying computer science at the University of Bristol after taking quite a varied set of subjects at A Level. I have always enjoyed helping others when it comes to school. Since I came to university I have bee...”

About the author

£20 /hr

Ta J.

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Chemistry

“About me Hi there, my name is Jin , and currently I am taking an undergraduate degree course for chemical engineering at the University Of Bath. For a long time now, I have always been keen on teaching people and passing on the knowled...”

MyTutor guarantee

You may also like...

Other A Level Maths questions

How do you find the inverse of a function?

Integrate 1/(5-2x) for 3≤x≤4

How would you sketch the curve of a graph?

What is the equation of the curve that has gradient dy/dx=(4x-5) and passes through the point (3,7)?

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

mtw:mercury1:status:ok