Integral of ∫cos^3(x)dx

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In this video, I work through the steps to solving the integral of cos^3(x) or [cos(x)]^3.

Note that because cos(x) is a function of x, not a mere polynomial, we can't just use the power formula as a method of integration. We must change the integrand cos^3(x) into a form that we can integrate.

We can do this by writing cos^3(x) as cos^2(x)cos(x). Then by recognising that cos^2(x) = 1 - sin^2(x), we have:

cos^3(x) = (1 - sin^2(x))cos(x)

Then we can simply use a u-substitution where u = sin(x) to complete the integral.

Thanks for watching. Please give me a "thumbs up" if you have found this video helpful.

Please ask me a maths question by commenting below and I will try to help you in future videos.

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I was solving a question and used th cos3x formula. I saw the answer and it was completely different than mine. Now, I have understood what they did. Thanks!

harshvardhanmisal

clear and excellent explanation. Thank you so much.

gilmaferrer

what is the solution of Integration cos^3(3x)dx?

sojibtushar

Sir can you plz help me solve a specific problem?
Question: Integrate cos3x using integration by parts with respect to x.

zhapuzep

Ezbere yapmamanız beni çok memnun etti 👍

wonderfulworld

Why we can't use chain rule for the cos function..??

cosmolearner

Hello. I doubt you still reply, but why aren't we able to directly use U-Substitution from the very start by setting U = Cos(x). Then use the power rule to get U^4/4

Anonymous

what is dy/dx(sinx-(sinx)^3/3+C)? It's difficult to calculate, it cant change to (cosx)^3, I got stuck by cosx-1+(cosx)^2

小白-mp

thank you so much, you are awesome ♥️

bibianarocha

I'm start watching your videos. Now i find myself getting a hope to do integration thanks for your wonderful companion.

susilxavier

x'=1 so (cos(x))^3*1 = f cos(u)^3 du = [ (cos(x))^4 ]/4, is that correct

小白-mp

Makes sense to me, but can anyone explain why it's vastly different to the answer Wolfram spits out?

poopensn

Is (1-sin^2(x))cos^2(x) able to be differentiated because the cos^2(x), which acts as the du in u substitution, is present? If that cos^2x wasn’t there then the du would have to be divided by cos^2x and that would be an issue for actually intergrating the whole function with u substitution right?

tristanjohnson

Your solution is wrong firstly it will be cos^3x=4cos^3x-3cosx then it will solve with other method

hanumantraonaidu

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