\begin{align}
\left[\frac{-2 b^2 s^2 \log \left(\frac{b \left(a+s^2\right)}{a}\right)-2 a b^2 \log \left(\frac{b \left(a+s^2\right)}{a}\right)
+2 b^2 s^2 \log \left(a+s^2\right)+2 a b^2 \log \left(a+s^2\right)
+2 b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \text{Ei}\left(-\frac{b \left(s^2+a\right)}{a}\right)+2 b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \log \left(\frac{b \left(a+s^2\right)}{a}\right)-2 b s^2 \log \left(\frac{b \left(a+s^2\right)}{a}\right)-2 a b \log \left(\frac{b \left(a+s^2\right)}{a}\right)-b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \log \left(-\frac{b \left(a+s^2\right)}{a}\right)-2 (b+1) b \left(a+s^2\right) \log \left(\frac{a}{b}\right)+2 b s^2 \log \left(a+s^2\right)+2 a b \log \left(a+s^2\right)+b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \log \left(-\frac{a}{b \left(a+s^2\right)}\right)+2 a}{2 a p},\Re\left(a+s^2\right)>0\land \left(\left(\Re\left(\frac{b}{a}\right)\geq 0\land \frac{b}{a}\neq 0\right)\lor \frac{b}{a}\notin \mathbb{R}\right)\right]
\end{align}
答案1
一些版本供您使用,
\begin{align}
\int_{\alpha=0}^{\infty}\lambda_1\lambda_2&\exp(-\lambda_1z)\frac{1} {\lambda_1 z+b}\frac{\exp(-\alpha h_{T_x,1}^2)}{p}d\alpha\nonumber\\
=&
\left.-2 b^2 s^2 \log \left(\frac{b \left(a+s^2\right)}{a}\right)-2 a b^2 \log \left(\frac{b \left(a+s^2\right)}{a}\right)+2 b^2 s^2\right.\nonumber\\
&\times \log \left(a+s^2\right)+2 a b^2 \log \left(a+s^2\right)+2 b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \text{Ei}\left(-\frac{b \left(s^2+a\right)}{a}\right)\nonumber\\
&+2 b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \log \left(\frac{b \left(a+s^2\right)}{a}\right)-2 b s^2 \log \left(\frac{b \left(a+s^2\right)}{a}\right)-2 a b \log \left(\frac{b \left(a+s^2\right)}{a}\right)\nonumber\\
&-b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \log \left(-\frac{b \left(a+s^2\right)}{a}\right)-2 (b+1) b \left(a+s^2\right) \log \left(\frac{a}{b}\right)+2 b s^2 \log \left(a+s^2\right)\nonumber\\
&+2 a b \log \left(a+s^2\right)+b s^2 e^{\frac{b \left(a+s^2\right)}{a}} \log \left(-\frac{a}{b \left(a+s^2\right)}\right)+2 a{2 a p},\Re\left(a+s^2\right)>0\nonumber\\
&\land \left(\left(\Re\left(\frac{b}{a}\right)\geq 0
\land \frac{b}{a}\neq 0\right)\lor \frac{b}{a}\notin \mathbb{R}\right)
\end{align}
答案2
我建议尽可能避免使用二层分数,尤其是指数。
另外,分母可以放在开头,并且条件可以单独添加在一行上。
\documentclass{article}
\usepackage{amsmath,amssymb}
\DeclareMathOperator{\Ei}{Ei}
\begin{document}
\begin{align*}
\frac{1}{2ap}\biggl(
&
-2 b^2 s^2 \log(b(a+s^2)/a)
-2 a b^2 \log(b (a+s^2)/a)
+2 b^2 s^2 \log(a+s^2)
\\
&
+2 a b^2 \log (a+s^2)
+2 b s^2 e^{b(a+s^2)/a} \Ei(-b(s^2+a)/a)
\\
&
+2 b s^2 e^{b(a+s^2)/a} \log(b(a+s^2)/a)
-2 b s^2 \log(b(a+s^2)/a)
\\
&
-2 a b \log(b(a+s^2)/a)
-b s^2 e^{b(a+s^2)/a} \log (-b(a+s^2)/a)
\\
&
-2 (b+1) b(a+s^2) \log(a/b)
+2 b s^2 \log(a+s^2)
+2 a b \log(a+s^2)
\\
&
+b s^2 e^{b(a+s^2)/a} \log\Bigl(-\frac{a}{b(a+s^2)}\Bigr)
+2 a
\biggr)
\\[2ex]
&\Re\left(a+s^2\right)>0 \land
\left(\left(\Re\left(\frac{b}{a}\right)\geq 0 \land
\frac{b}{a}\neq 0\right)\lor \frac{b}{a}\notin \mathbb{R}\right)
\end{align*}
\end{document}