# improper integral of (2^(ln(n)))^-1

• August 27th 2010, 07:53 PM
RedSwiss
improper integral of (2^(ln(n)))^-1
I don't understand how they get this boxed in quantity (shown in attachment)
• August 27th 2010, 08:06 PM
Prove It
$\int{\frac{dx}{x^{\ln{2}}}} = \int{x^{-\ln{2}}\,dx}$

$= \frac{x^{-\ln{2} + 1}}{-\ln{2} + 1}$

which gives you the required stuff inside the box.
• August 27th 2010, 08:09 PM
RedSwiss
is this some linearity of limits trick?
• August 27th 2010, 08:20 PM
RedSwiss
furthermore
can someone tell me why 1^(1-ln(2)) = 1 ????
• August 27th 2010, 08:23 PM
Prove It
Because 1 to the power of anything is 1.