Finding function (integration)

TsAmE

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

mr fantastic

MHF Hall of Fame
Find a function f such that f(1) = 0 and f'(x) = 2^(x) / x
$$\displaystyle f(x) = \int_1^x \frac{2^t}{t} \, dt$$.

General and skeeter

skeeter

MHF Helper
$$\displaystyle f(x) = \int_1^x \frac{2^t}{t} \, dt$$.
I love it when it's simple ... (Clapping)

TsAmE

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

mr fantastic

MHF Hall of Fame
Arent you suppose to find the anti-derivative of f'(x) = 2^(x) / x?
In that case, good luck ....

TsAmE

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

General

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 ..

mr fantastic