Integral of sin^3x

This calculus video tutorial explains how to find the integral of sin^3x using the pythagorean identities of trigonometry and integration by u-substitution. You also need to be familiar with the basic power rule for integration and finding antiderivatives.

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[ibrarkhan]

Thank you. I just pondered upon this integral for one hour but I didn't figure it out. Thank you once again so much.

[amitavmostafa]

The most slept on education channel on YouTube

[pippinhart]

The way I labored over this problem for like half an hour because I didn't realize you could pick cosx as u instead of cos^2x... 😶

[jimcar]

I also had a lot of trouble with this problem. Once again, your explanations are brilliant and very helpful. Thank you very much..

[successthruknowledge]

Found this from your sin^2(x) integral video. Another nice and succinct video👍

[KEQI-zvjm]

1:04 how do u know u is equal to cosx rather than sinx

[LogintoMaths]

We can use the formula sin3x = 3sinx-4sin³x, further get the value of sin³x

[mezonei]

just a question why did the negative sign didnt effect constant ?

[mamta]

why not take sin x =r then we have to integrate r^3 dr/cosx while integrating cosx come out as it it constant for what we are integrating

[Vansh-tz]

I am from hindi medium but I understand very.clearly thanks sir 🙏🏻 ❤ and your voice is soo sweet i like to hear your voice ❤😊

[uditnarayan]

Can we also solve it
by using identity of sin3x ?

[Blaster]

Is there a method where you can use integration by parts?

[عبدالحميد-ظه]

Thank you so much I have final tomorrow .

[iloveyouheeseung]

how can i put these informations in my head

[Marshark]

My teacher made this more confusing then it had to be using some weird notation, thank you

[manishseeruthun]

But surely you do not necessarily have to do substitution?

Instead of turning sin^2(x) into [1-cos^2(x)] you could use the double angle formula, where cos(2x) = cos^2(x) - sin^2(x) and thus with the use of sin^2(x) + cos^2(x) = 1 you can deduce that cos(2x)= 1 - 2sin^2(x).

Then you could rearrange for sin^2(x) = 1/2 - 1/2 cos(2x) and use that in the integral instead. I guess it is still a substitution per se but it doesn't require you to use the 'Integration by Substitution' method via the use of 'u'. I honestly prefer it this way, but I guess it depends on whatever suits you. Do you think this way is better? EDIT: Actually, I may have made life harder for myself, as you may have to do integration by parts later on anyway...

[christine.]

I dont understand why you have not added 1/2 here but you did when you expanded it before

[ethanscott]

why is the antiderivative for 1 u and not x?

[flightyavian]

I hate and love how the integral of sin³x is so much easier than sin²x.... No double angle needed, just turn it into (sinx - sinxcos²x) and from my experience with derivatives, i can immediately tell that since the function that has the power on it is multiplied with it's derivative, that i can just add onto the power and divide by it. Chain rule and it's reverse!
Meanwhile expanding sin²x into 1-cos²x doesn't help...

[thunder]

Cannot we imagine that u = sin(x)
????