As mentioned, WordPress does not provide general LaTeX support, but usually only mathmode support. Thus you have to use something that works from within mathmode, and not its own environemnt. In this case, there is a very useful one called ‘aligned’ (with the ‘ed’ at the end). To render the above in your default WordPress.com LaTeX (or even in MathJax-LaTeX plug-in), use the following code:
$latex
\begin{aligned}
\int \frac{1}{(2x^{2}+4x-2)^{-\frac{3}{2}}} \ \textrm{dx} &= \frac{\sqrt{2}}{8} \int\frac{\sec{t} \cdot \tan{t}}{\tan^{3}{t}} \ \textrm{dt} \\ &= \frac{\sqrt{2}}{8} \int\frac{\cos{t}}{\sin^{2}{t}} \ \textrm{dt}
\end{aligned}
$
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