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# Integral help??????!!!!????

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1. I'm back with another integral, it's been a while, posted this somewhere else but may as well make a thread.

(i) Integrate with respect to .

(ii) Hence, or otherwise, evaluate the integral
,
leaving your answer in a simplified exact form.
2. (Original post by Ano123)
I'm back with another integral, it's been a while, posted this somewhere else but may as well make a thread.

(i) Integrate with respect to .
Note that:

3. (Original post by Zacken)
Note that:

How did you do it by inspection? Seen similar types before or just recognised it was the derivative of a relatively simple function?
4. (Original post by Ano123)
How did you do it by inspection? Seen similar types before or just recognised it was the derivative of a relatively simple function?
Just recognised. Shouldn't be too hard to do as a geometric series with a first term and common ratio either.
5. (Original post by Zacken)
Just recognised. Shouldn't be too hard to do as a geometric series with a first term and common ratio either.
I should have made it more difficult with a square root or something.
6. (Original post by Ano123)
I should have made it more difficult with a square root or something.
*shrugs* indefinite integrals are boring. It means that an elementary anti-derivative exists which is a buzzkill assumption.
7. (Original post by Zacken)
*shrugs* indefinite integrals are boring. It means that an elementary anti-derivative exists which is a buzzkill assumption.
What would you prefer then?
8. (Original post by Ano123)
What would you prefer then?
Definite ones, then elementary antiderivatives need not exist.

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