# Integral

• Dec 29th 2012, 10:05 AM
jones123
Integral
Hello! How would you integrate 2^x / ln2? Thanks already!
• Dec 29th 2012, 10:21 AM
a tutor
Re: Integral
$\displaystyle 2^x=e^{\ln 2^x}=e^{x \ln 2}$
• Dec 29th 2012, 10:38 AM
Deveno
Re: Integral
note that:

$\frac{1}{\ln(2)} = \frac{\ln(2)}{(\ln(2))^2}$

you can take the denominator (which is just a constant) outside the integral, so:

$\int \frac{2^x}{\ln(2)}\ dx = \frac{1}{(\ln(2))^2}\int \ln(2)2^x\ dx = \frac{1}{(\ln(2))^2} \int e^{\ln(2)x} \ln(2)\ dx$

if you use the substitution $u = \ln(2)x$ what would $du$ be?