Need helping integrating...

**ArTiCK** · September 23rd 2009, 02:41 AM

Hi all,

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

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.

Thanks in advance,
ArTiCk

**Danny** · September 23rd 2009, 03:04 AM

Originally Posted by ArTiCK

Hi all,

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

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.

Thanks in advance,
ArTiCk

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

$\int 4^{-x}\,dx = - \frac{1}{\ln4} \int u \cdot \frac{du}{u} = - \frac{1}{\ln4} \int du$ .

I believe you can take it from here.

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