# Finding function (integration)

• May 8th 2010, 01:15 PM
TsAmE
Finding function (integration)
Find a function f such that f(1) = 0 and f'(x) = 2^(x) / x
• May 8th 2010, 02:49 PM
mr fantastic
Quote:

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

$f(x) = \int_1^x \frac{2^t}{t} \, dt$.
• May 8th 2010, 03:46 PM
skeeter
Quote:

Originally Posted by mr fantastic
$f(x) = \int_1^x \frac{2^t}{t} \, dt$.

I love it when it's simple ... (Clapping)
• May 9th 2010, 02:27 AM
TsAmE
Arent you suppose to find the anti-derivative of f'(x) = 2^(x) / x?
• May 9th 2010, 02:52 AM
mr fantastic
Quote:

Originally Posted by TsAmE
Arent you suppose to find the anti-derivative of f'(x) = 2^(x) / x?

In that case, good luck ....
• May 10th 2010, 12:02 PM
TsAmE
Quote:

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
• May 10th 2010, 01:07 PM
General
Mr F did not use any method ..

He get the answer by using the FTC ..

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

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