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# C4 Integration watch

1. I am not sure why the integral of sec^(2)xtan^(2)x is 1/3tan^(3)x.
Please can anyone show me the steps to get there. Much appreciated!
2. (Original post by QueenOfNachos)

I am not sure why the integral of sec^(2)xtan^(2)x is 1/3tan^(3)x.
Please can anyone show me the steps to get there. Much appreciated!
Well, think of a substitution.
3. (Original post by zetamcfc)
Well, think of a substitution.
Ah yes. How did I not think of that. Got it now, thanks a lot!!
4. (Original post by QueenOfNachos)

I am not sure why the integral of sec^(2)xtan^(2)x is 1/3tan^(3)x.
Please can anyone show me the steps to get there. Much appreciated!

.

Can you finish this?
5. (Original post by atsruser)

.

Can you finish this?
Yes I can, thank you very much!
6. (Original post by QueenOfNachos)

I am not sure why the integral of sec^(2)xtan^(2)x is 1/3tan^(3)x.
Please can anyone show me the steps to get there. Much appreciated!
I'm a bit late to the party, but I prefer to do these integrals by recognition (also referred to as "reverse chain rule" rather than substitution - it's a little quicker than using a sub. I'll show you what I mean.

We know that via the chain rule, right? Since we know the derivative of this, we can say that
Won't be too tough finding the integral from here, I hope!
Spoiler:
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