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I haven't taken Calculus for a while, but isn't integration inverse derivative?

The derivative of x[sup]1[/sup] = 1, so the integral of 1 should be x[sup]1 [/sup]right?
Strangely, the derivative of e[sup]x[/sup] = e[sup]x[/sup] so naturally it would be its own integral, right?

That would mean the integral is something like (x + e[sup]x[/sup])?

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Maths has always been one of my best subjects at school and although I had a very significant amount of time off this year I found the AS wasn't too hard either. I have had a lot of moments where I have been stunned that some people found some of it as hard as they did, and helped my friends on numerous occasions. Shame how in the last few years I've stopped being the statistical best in my year, but frequent illness probably didn't help that.

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[quote name='Expelsword - 信仰' timestamp='1338729368' post='5951478']
I haven't taken Calculus for a while, but isn't integration inverse derivative?

The derivative of x[sup]1[/sup] = 1, so the integral of 1 should be x[sup]1 [/sup]right?
Strangely, the derivative of e[sup]x[/sup] = e[sup]x[/sup] so naturally it would be its own integral, right?

That would mean the integral is something like (x + e[sup]x[/sup])?
[/quote]

Not really. The actual function you're integrating would be:

[u][color=#ffffff]00[/color]1 [/u]
1+e[sup]x[/sup]

Not just (1 + e[sup]x[/sup]).

If you just did it by (1+e[sup]x[/sup])[sup]-1[/sup] and tried to use power rule, you'd miss out on chain rule.

If you try using integration by parts, you get a disgustingly messy du value.

The actual way in which you'd do this integral is really obscure, though it was a challenging problem.

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[quote name='Dark' timestamp='1338700644' post='5951384']
This question baffled me for ten minutes until I saw the trick.

Find the indefinite integral of [dx / (1 + e^x)]

No hints. And don't use Wolfram Alpha. I'll give you a cookie if you figure it out.
[/quote]

If I'm completely wrong, slap me. I did well with these in school, but it's been far to long. So I'm going to throw out a guess here.

EDITED AS I'M PUTTING SOMETHING ELSE!

I feel like I missed something. .-.

-1/2 (1+e) - 1/e

THAT'S MY FINAL ANSWER!

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Catman, my school used to have 20-30 digits of it running along the top of the Maths corridor, it was gone before I left though. The only Science I passed at AS didn't have that much Maths in, until I had to work out statistics as part of my pratical coursework in A Level (Biology =D)

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[quote name='Dwarven King' timestamp='1338782675' post='5951785']
If I'm completely wrong, slap me. I did well with these in school, but it's been far to long. So I'm going to throw out a guess here.

EDITED AS I'M PUTTING SOMETHING ELSE!

I feel like I missed something. .-.

-1/2 (1+e) - 1/e

THAT'S MY FINAL ANSWER!
[/quote]

Uh... how exactly did you arrive at that answer?

You don't have any variables, and it's an indefinite integral.

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Tch, no calculus for me till fourth semester... I heard they made a science club for the special kids in my school where they allegedly see some more advanced stuff. I could have gotten there if I hadn't skipped class so much.

It shouldn't be that hard; I was sorted with most of those guys in first semester and sincerely, they were kinda thick.

Whatever, math and most sciences come as easy as breathing to me~

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[quote name='Yin' timestamp='1339444389' post='5955525']
Catman, my school used to have 20-30 digits of it running along the top of the Maths corridor, it was gone before I left though. The only Science I passed at AS didn't have that much Maths in, until I had to work out statistics as part of my pratical coursework in A Level (Biology =D)
[/quote]

catman is his first account the second account is adam west xd (tv show reffence)

i was very good at math science but english not my first thang or lang so whatevers

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