Integrating using the reverse chain rule

Can anyone explain how to integrate sec^2xtan^2x using the reverse chain rule and the same with xe^x^2?

I can do all of the other questions using the reverse chain rule but not these two and there isn't really any useful explanations, on the reverse chain rule, out there.

Reply 1

mqb2766

Original post

by m_ahmed_w

Can anyone explain how to integrate sec^2xtan^2x using the reverse chain rule and the same with xe^x^2?
I can do all of the other questions using the reverse chain rule but not these two and there isn't really any useful explanations, on the reverse chain rule, out there.

Reverse chain rule is just simple substitution, so if you cant see how to do it directly, think about writing a substitution out fully. Both are reasonably clear thinking about what the substution could be and what its derivative is.

Reply 2

tonyiptony

Original post

by m_ahmed_w

Can anyone explain how to integrate sec^2xtan^2x using the reverse chain rule and the same with xe^x^2?
I can do all of the other questions using the reverse chain rule but not these two and there isn't really any useful explanations, on the reverse chain rule, out there.

To expand on mqb's comment, the idea of "inverse chain rule" is to spot (!!) that the integrand is of the form $u'f(u)$ . What do you think $u$ is in each case? Note that for first-timers to integration, trial and error is often required.

Anyhow, the safe thing to do is substitution, as spotting the form is not easy for most people.

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