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Integration a level edexcel question

https://imgur.com/a/69q6YmN

Can anyone help me with this? I’m not sure if I’ve done it correctly
Reply 1
Original post by username79352
https://imgur.com/a/69q6YmN
Can anyone help me with this? I’m not sure if I’ve done it correctly

No. You divide by e^x when equating the integrand/integral in the middle which is a function of x. It would be ok if it was a constant. As a check try differentiating your final answer (e^x+1)^3 / 3e^x

You seem to lay out your answers for reverse chain like this, so Id think about how you write it down so it catches such problems.

Looks like a substitution would be in order or expand and do each term seperately. The latter is probably the most elementary.
(edited 4 weeks ago)
Reply 2
This question looks a bit like inverse chain rule but inverse chain rule require the kernel of the integral to contain a product of two functions, one is a composite fg(x) and the other is the differential of the inner function g’(x). If you see this form then you can use inverse chain rule directly. Often, g’(x) can be generated algebraically but this is usually only helpful if the g’(x) is a constant. Assuming g’(x) is a constant k, Then you can just say k . 1/k = 1 and put k outside the integral and 1/k inside but the g’(x) is itself a function of x then you would need to put something involving x outside the integral (which is absolutely not ok).

Hence, in this case you need to expand the bracket and integrate term by term.

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