# Math Help - Please show me the steps to this integration...

1. ## Please show me the steps to this integration...

Could somebody please walk me through this integration, thank-you.
$\int{\alpha^\beta x^{-\beta-1}d\beta}$

2. Hello, tDM!

$\int{\alpha^\beta x^{-\beta-1}d\beta}$
The variables are very confusing . . . I'll modify the problem.

. . $\int a^xb^{-x-1}\,dx$ . . .There! ... $a$ and $b$ are constants, $x$ is the variable.

We have: . $a^xb^{-(x+1)} \:=\:\frac{a^x}{b^{x+1}} \;=\;\frac{a^x}{b\cdot b^x} \;=\;\frac{1}{b}\cdot\frac{a^x}{b^x} \;=\;\frac{1}{b}\left(\frac{a}{b}\right)^x$

Therefore: . $\frac{1}{b}\int\left(\frac{a}{b}\right)^xdx \;=\;\frac{1}{b}\cdot\frac{\left(\frac{a}{b}\right )^x}{\ln\left(\frac{a}{b}\right)} + C \;=\;\frac{1}{b\ln(\frac{a}{b})}\cdot\left(\frac{a }{b}\right)^x + C$