Maths C4 - Integration... Help???

Yes it is. Look at all the information, there is one equality that shows they're both the same.

Ohhh because of $a^x = e^{x\ln a}$

But then where is the equality above derived from?

Ohhh because of $a^x = e^{x\ln a}$

But then where is the equality above derived from?

The fact that $e^{\ln(a)}=a$ and that $x\ln(a)=\ln(a^x)$ - just basic log rules from C2

Didn't you ask this on TSR before and there were quite a few posts explaining it? Or am I mixing you up with someone else?

Didn't you ask this on TSR before and there were quite a few posts explaining it? Or am I mixing you up with someone else?

Great now I'm trying to see how $a^x = e^{x\ln a}$ is derived from...

$e^{\ln(a)}=a$ and $x\ln(a)=\ln(a^x)$

I can't recall me asking this before, but knowing me it might have been!

Is there a video anywhere explaining it?

Yeah it was him



https://www.thestudentroom.co.uk/showthread.php?t=4642162

Have a look through this thread

Oh dear, why do I have the memory of a sieve?! Sorry about this

Also I have no idea how $a^x = e^{x\ln a}$ is linked to the above Seriously feel like giving up this close to the exams!

If you're still unsure about it then it would be worth going through that thread and quoting posts that you don't understand.

Great now I'm trying to see how $a^x = e^{x\ln a}$ is derived from...

$e^{\ln(a)}=a$ and $x\ln(a)=\ln(a^x)$

I feel so stupid! I spent so long trying to figure this out over something that is actually so so so simple!! Thanks for clearing this up!




Yeah I'm definitely still trying to get to grips with $f'(x)[f(x)]^n = \frac{[f(x)]^{n+1}}{n+1} + c$

It may take me a while

Sorry if this is obvious at all, but you see that if you differentiate the right side how everything fits together. First bring down the power, this cancels the 1/(n+1).
Then you decrease the power, giving n.
Now here's the important bit, the chain rule. f(x)^(n+1) is in essence another function, let's call it g(x). You just differentiated g(x) when you brought down the power and reduced it. Now we have to differentiate the function within the function and multiply it with g'(x). That's where the f'(x) is from.

I hope this helps. Good luck with nailing c4!

Slightly confusing, but I think I get what you're saying. It's difficult to understand without an actual example though

You've been doing these examples...

Yeah but I haven't tried using the fact that $\int f'(x)[f(x)]^n = \frac{[f(x)]^{n+1}}{n+1} + c$ in reverse

Yeah you have. It's just the chain rule.

Oh really? Why am I having a hard time recognising it from that formula?