$$ \begin{align} \int^{1}_{0}\int^{\sqrt{1-y^2}}_{0}\int^{\sqrt{x^2+y^2}}_{x^2+y^2} xyz dz dx dy &= \int^{\frac{\pi}{2}}_{0}\int^{1}_{0}\int^{r}_{r^2} r^2z \sin{\theta}\cos{\theta} dz \cdot rdr d\theta \newline &= \frac{1}{2}\int^{1}_{0} r^5-r^7 dr \cdot \int^{\frac{\pi}{2}}_{0}\sin{\theta}\cos{\theta} d\theta \newline &= \frac{1}{2} \left[ \frac{1}{6}r^6 - \frac{1}{8}r^8 \right]^{1}_{0} \cdot \int^{0}_{\frac{\pi}{2}}\cos{\theta} d\cos{\theta} \newline &= \frac{1}{4}\cdot \left[ \frac{1}{6} - \frac{1}{8} \right] \newline &= \frac{1}{96} \end{align} $$

Step 1:

新增**/layouts/partials/MathJax.js**

<script type="text/javascript"
  src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/latest.js?config=TeX-MML-AM_CHTML" async>
    MathJax.Hub.Config({
      tex2jax: {
        inlineMath: [['$', '$'], ['\\(', '\\)']],
        displayMath: [['$$', '$$'], ['\[', '\]']],
        processEscapes: true,
        processEnvironments: true,
        skipTags: ['script', 'noscript', 'style', 'textarea', 'pre'],
        TeX: {
          equationNumbers: { autoNumber: "AMS" },
          extensions: ["AMSmath.js", "AMSsymbols.js"]
        }
      }
    });
    MathJax.Hub.Queue(function () {
      // Fix <code> tags after MathJax finishes running. This is a
      // hack to overcome a shortcoming of Markdown. Discussion at
      // https://github.com/mojombo/jekyll/issues/199
      var all = MathJax.Hub.getAllJax(), i;
      for (i = 0; i < all.length; i += 1) {
        all[i].SourceElement().parentNode.className += ' has-jax';
      }
    });
  </script>
<style>
  code.has-jax {
    font: inherit;
    font-size: 100%;
    background: inherit;
    border: inherit;
    color: #515151;
  }
</style>

Step 2:

在外框layout的header加入

{{ partial "MathJax.html" . }}

Notes:

要用 \_ 代替 _

要用 \newline 不能用 \\

References:

https://divadnojnarg.github.io/blog/mathjax/

https://www.gohugo.org/doc/tutorials/mathjax/