how do you integrate 1 over 2^x?

Question

I need to integrate 1 over 2^x    1/2^x dx

Answer 1

u = 1/2^x

du/dx = ln(2)/2^x

dx = 2^x/ln(2) du

=> 1/2^x dx = (1/2^x) (2^x/ln(2)) du = 1/ln(2) du

integrate du = u + c

=> answer = 1/(ln(2) 2^X) + c

Comments

forgot a - sign...

du/dx = - ln(2)/2^x