# Need helping integrating...

• September 23rd 2009, 03:41 AM
ArTiCK
Need helping integrating...
Hi all,

I need help integrating the following:
$
\int \frac {1}{4^x} dx
$

I know that d/dx(a) = ln(a)a^x. However i wondering if anyone could show me the steps of integration for the above without recognition.

ArTiCk
• September 23rd 2009, 04:04 AM
Jester
Quote:

Originally Posted by ArTiCK
Hi all,

I need help integrating the following:
$
\int \frac {1}{4^x} dx
$

I know that d/dx(a) = ln(a)a^x. However i wondering if anyone could show me the steps of integration for the above without recognition.

let $u = 4^{-x}$ so $\ln u = -x \ln 4$. Further $-\frac{1}{\ln 4} \cdot \frac{du}{u} = dx$. Your integral becomes
$\int 4^{-x}\,dx = - \frac{1}{\ln4} \int u \cdot \frac{du}{u} = - \frac{1}{\ln4} \int du$.