1. ## Finding function (integration)

Find a function f such that f(1) = 0 and f'(x) = 2^(x) / x

2. Originally Posted by TsAmE
Find a function f such that f(1) = 0 and f'(x) = 2^(x) / x
$\displaystyle f(x) = \int_1^x \frac{2^t}{t} \, dt$.

3. Originally Posted by mr fantastic
$\displaystyle f(x) = \int_1^x \frac{2^t}{t} \, dt$.
I love it when it's simple ...

4. Arent you suppose to find the anti-derivative of f'(x) = 2^(x) / x?

5. Originally Posted by TsAmE
Arent you suppose to find the anti-derivative of f'(x) = 2^(x) / x?
In that case, good luck ....

6. Originally Posted by mr fantastic
In that case, good luck ....
I am not sure of the method you used, thats why I asked, as I thought that the only of finding it was by using an anti-derivative

7. Mr F did not use any method ..

He get the answer by using the FTC ..

The problem here is that $\displaystyle \int \frac{2^x}{x} \, dx$ is unelementary integral ..

What ever you do, you can not evaluate it in terms of elementary functions ..