How do you integrate e^x cos x

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / How do you integrate e^x cos x

1113 views

How do you integrate e^x cos x

∫ e^xcos 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 = e^x

du/dx = -sin x and v= e^x

∫ e^xcosx dx = e^xcos x - ∫ e^x (-sin x) dx
= e^xcos x + ∫ e^xsinx dx

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

du/dx = cos x and v= e^x

∫ e^x cos x dx = e^xcos x + ( e^x sin x - ∫ e^x cos x dx )

2 ∫e^xcos x dx = e^xcos x + e^xsin x
∫ e^x cos x dx = 1/2 ( e^xcos x + e^x 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

306 SUBJECT SPECIALISTS

£36 /hr

Ignacio P.

Degree: Aerospace Engineering MEng (Masters) - Bristol University

Subjects offered:Maths, Spanish+ 5 more

“Author of The 3-Step Method to Achieving (under publishing) - APPLIED NEUROSCIENCE & COACHING FOR EXPLOSIVE RESULTS IN MATH, PHYSICS, SPANISH & MORE!”

5.0

4 reviews | 3 completed tutorials

Save profile

Mark H. GCSE Maths tutor, A Level Maths tutor, GCSE Physics tutor

View profile

£24 /hr

Mark H.

Degree: Mathematics MMath (Masters) - Manchester University

Subjects offered:Maths, Physics+ 1 more

“Hello there, I'm Mark and I study Mathematics at the University of Manchester! Let me help you achieve your best! ”

5.0

60 reviews | 80 completed tutorials

Save profile

Graeme D. GCSE Physics tutor, A Level Physics tutor, IB Physics tutor

View profile

£20 /hr

Graeme D.

Degree: PhD Physics (Doctorate) - St. Andrews University

Subjects offered:Maths, Physics

“I am a PhD student at the University of St Andrews studying nonlinear optics. I enjoy discussing physics and get pleasure from helping others”

5.0

2 reviews | 9 completed tutorials

Save profile

See more A Level Maths tutors

About the author

View profile

£20 /hr

Ta J.

Degree: Chemical Engineering (Masters) - Bath University

Subjects offered:Maths, Further Mathematics + 1 more

“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

Save profile

Version:	3.45.0
Build:	16acc337b3ec
Time:	2017-06-13T06:44:00Z

MYTUTOR SUBJECT ANSWERS

How do you integrate e^x cos x

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

306 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips