How do I integrate cos^2(x)?

The key to solving any integral of this form is to use the cosine rule:

cos(2x) = cos2(x) - sin2(x) = 2cos2(x) - 1 = 1 - 2sin2(x)

All of these forms are really helpful when solving problems such as this, and it's great if you can remmeber them, though if you get stuck in an exam, they can all be derived from the addition formulae that are probably on your fomula sheet!

So, using the above idenities, we know that:

2cos2(x) - 1 = cos(2x)

2cos2(x) = cos(2x) + 1

cos2(x) = (cos(2x) + 1)/2

So instead, we perform the integral of (cos(2x) + 1)/2, which we already know how to do.

=> (sin(2x))/4 + x/2

Daniel F. A Level Maths tutor, A Level Further Mathematics  tutor, GC...

2 years ago

Answered by Daniel, an A Level Maths tutor with MyTutor

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


£22 /hr

Laura L.

Degree: Chemistry (MCHEM) (Masters) - Warwick University

Subjects offered:Maths, Chemistry+ 1 more


“Hi there! I'm a third-year Chemistry student, I tutor maths from 11+ to A level as well as GCSE Science, A level Biology, and Chemistry”

Sam C. GCSE Maths tutor, 13 Plus  Maths tutor, 11 Plus Maths tutor, A...
£20 /hr

Sam C.

Degree: Physics (Masters) - Oxford, Trinity College University

Subjects offered:Maths, Physics+ 2 more

-Oxbridge Preparation-

“Maths and Physics hold the tools to unravelling the mysteries of the universe! I hope you enjoy unlocking these tools as much as I do!”

£30 /hr

James T.

Degree: Economics & Management (Bachelors) - Bristol University

Subjects offered:Maths, Economics


“I am currently studying Economics & Management at the University of Bristol, and love working with students of all ages, specialising in Maths and Economics at both A-Level and GCSE. I have been teaching drums and coaching tennis for ...”

About the author

Daniel F.

Currently unavailable: for regular students

Degree: Maths and Philosophy (Bachelors) - Durham University

Subjects offered:Maths, Further Mathematics

Further Mathematics

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

You may also like...

Posts by Daniel

How do I integrate cos^2(x)?

How do I integrate log(x) or ln(x)?

Other A Level Maths questions

A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

How do you take the derivative of a^x ?

Solve x^2 + 8x +3 = 0 by completing the square.

The curve C has equation y = x^3 - 2x^2 - x + 9, x > 0. The point P has coordinates (2, 7). Show that P lies on C.

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