MYTUTOR SUBJECT ANSWERS

1654 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...

2 years ago

Answered by Ta, an A Level Maths tutor with MyTutor


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

361 SUBJECT SPECIALISTS

Roma V. A Level Maths tutor, 13 Plus  Maths tutor, GCSE Maths tutor, ...
£26 /hr

Roma V.

Degree: Mathematics, Operational Research, Statistics and Economics (Bachelors) - Warwick University

Subjects offered:Maths, Further Mathematics + 1 more

Maths
Further Mathematics
Economics

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

£26 /hr

Scott R.

Degree: PGCE Secondary Mathematics (Other) - Leeds University

Subjects offered:Maths, Further Mathematics

Maths
Further Mathematics

“I am currently completing 2 PGCEs in Leeds. I have always had a passion for maths and my objective is to help as many as possible reach their full potential.”

£26 /hr

Prina S.

Degree: Environmental Geoscience (Masters) - Bristol University

Subjects offered:Maths, Physics+ 2 more

Maths
Physics
Geography
Biology

“Hello there! My name is Prina and I love studying and tutoring maths and science. Check out my profile for how I teach and previous students' feedback!”

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

Solve the equation tanx/cosx = 1 for 0°<x<360°

How do you find the point or points of intersection of a straight line and a circle?

how do integrate an equation with a surd or a fraction?

Differentiate 4x^2 + 2ln3x + e^x

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