Problem with using multline and align

Question

I am LaTeX begginer and when I run this equation, I am getting the error:

! Argument \align* has an extra {. 

Here is the equation.

\begin{multline}
\begin{align*}
C_s & = \displaystyle \max_{P(g_M)} \int_0^{\infty} 
        \bigg[ \left(1-\exp\left(-\frac{g_M}{\overline{g}_W}\right) \right)
            \log\left(1+\frac{g_MP(g_M)}{N_M}\right)- \\
            \int_0^{g_M} \log\left(1+\frac{g_WP(g_W)}{N_W}\right)
            \frac{1}{\overline{g}_W}\exp\left(-\frac{g_W}{\overline{g}_W}\right)
        dg_W \bigg] 
        \frac{1}{\overline{g}_W}\exp\left(-\frac{g_M}{\overline{g}_M}\right) dg_M \\ 
    & = \max_{P(g_M)} \int_0^{\infty} 
        \bigg[\log \left(1+\frac{g_MP(g_M)}{N_M}\right) -
            \exp\left(\frac{1}{\overline{g}_WP(g_M)}\right)
            \bigg(Ei\left(\frac{1}{\overline{g}_WP(g_M)}\right)- \\
                  Ei\left(\frac{g_M}{\overline{g}_W}+
                  \frac{1}{\overline{g}_WP(g_M)}\right)
            \bigg)
        \bigg]
        \frac{1}{\overline{g}_M}\exp\left(-\frac{g_M}{\overline{g}_M}\right) dg_M 
\end{align*}
\end{multline}

Can someone please help? Thank in advance

Answer 1

This is probably close enough to what you are trying to achieve:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{align*}
\begin{split}
C_s & = \max_{P(g_M)} \int_0^{\infty} 
        \bigg[ \left(1-\exp\left(-\frac{g_M}{\overline{g}_W}\right) \right)
            \log\left(1+\frac{g_MP(g_M)}{N_M}\right) \\
    &\quad -\int_0^{g_M} \log\left(1+\frac{g_WP(g_W)}{N_W}\right)
            \frac{1}{\overline{g}_W}\exp\left(-\frac{g_W}{\overline{g}_W}\right)
        dg_W \bigg] 
        \frac{1}{\overline{g}_W}\exp\left(-\frac{g_M}{\overline{g}_M}\right) dg_M 
\end{split}\\ 
\begin{split}        
    & = \max_{P(g_M)} \int_0^{\infty} 
        \bigg[\log \left(1+\frac{g_MP(g_M)}{N_M}\right) 
            -\exp\left(\frac{1}{\overline{g}_WP(g_M)}\right)
            \bigg(Ei\left(\frac{1}{\overline{g}_WP(g_M)}\right) \\
    &\quad   -Ei\left(\frac{g_M}{\overline{g}_W}
                      +\frac{1}{\overline{g}_WP(g_M)}\right)
            \bigg)
        \bigg]
        \frac{1}{\overline{g}_M}\exp\left(-\frac{g_M}{\overline{g}_M}\right) dg_M 
\end{split}
\end{align*}

\end{document}

A couple of points:

• It is perfectly ok to use split inside align (see for instance this question).
• You should put the minus signs after line breaking.
• You don't need displaystyle as equations are already displayed in the align environment.
• You can improve the alignment by adding white space with \quad, \qquad or even \phantom.