Integrating Exponential Function (1 Viewer)

[pi-ka-chew]

How do I integrate 2^(log x)?
the textbook gave a little hint: "e^(log x) = x, so what is 2^log x?"
the hint didn't really help me.


please help. thanks in advance.

 

[shady145]

what's the base(i guess 2?)... the little number on the right of the log
the hint is obviously to the base e

 

[Trebla]

Note that: e^{ln 2} = 2

I am going to assume "log x" refers to the natural log, ln x.

2^{ln x} = e^{ln 2.ln x} = (e^{ln x})^{ln 2} = x^{ln 2}

You should now be able to integrate this form.