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


£20 /hr

Megan O.

Degree: MMath (Masters) - Exeter University

Subjects offered: Maths


“I'm Meg, and I am currently a 3rd year maths student at Exeter university. I have a huge passion for my subject, which i believe to be one of the most important qualities in a tutor. I have experience in both one to one and group tuto...”

£20 /hr

James K.

Degree: Law with Accounting and Finance (Bachelors) - Liverpool University

Subjects offered: Maths, Law+ 1 more

Business Studies

“About Me: I am currently studying Law with Accounting and Finance (LLB Hons) at the University of Liverpool. I have always had a real passion and love for Maths, Economics, Business and reccently discovered Law and hope that my tutori...”

MyTutor guarantee

£20 /hr

Ed W.

Degree: Medicine (Bachelors) - Edinburgh University

Subjects offered: Maths, Further Mathematics + 3 more

Further Mathematics
-Medical School Preparation-

“Hi! I'm Ed and I'm currently studying Medicine at the University of Edinburgh. I tutor at GCSE and A Level forBiology, Chemistry and Maths, and at GCSE level forFurther Maths. These are subjects I'm very comfortable in and enjoy. With ...”

MyTutor guarantee

About the author

£22 /hr

Daniel F.

Degree: Maths and Philosophy (Bachelors) - Durham University

Subjects offered: Maths, Further Mathematics

Further Mathematics

“Friendly and Enthusiastic Maths and Philosophy student at Durham University”

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

What is trigonometry? How do I remember sine, cosine and tangent?

Explain the Principle of Moments.

Differentiate y = (6x-13)^3 with respect to x

Show that 2sin(2x)-3cos(2x)-3sin(x)+3=sin(x)(4cos(x)+6sin(x)-3)

View A Level Maths tutors


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