Arrange Equations

Question

\[
  \begin{split}\int_{0}^{2\pi} &f(x)\cos(nx)dx =\frac{a_0}{2}\int_{0}^{2\pi}\cos(nx)dx\\
  &+a_1\boxed{\int_{0}^{2\pi}cos(x)\cos(nx)dx}+a_2 \boxed{\int_{0}^{2\pi}\cos(2x)\cos(nx)dx}+...\\
  &+a_n\boxed{\int_{0}^{2\pi}\cos^2(nx)dx} \\
  &+ b_1\boxed{\int_{0}^{2\pi}\sin(x)\cos(nx)dx} +b_2\boxed {\int_{0}^{2\pi}\sin(2x)\cos(nx)dx} + ...\\ &+b_n\boxed{\int_{0}^{2\pi}\sin(nx)\cos(nx)dx} 
  \end{split}
\]

Hi, I am still new in Latex and want some help.

If you run this code, you see a_n and b_n go to the second line. I want to keep a_1,a_2+...+a_n in one line so do b_1 and b_2,b_n.

I want to arrange them properly. I am still confused how to use & \ and split and other functions to arrange any equations.

your help is greatly appreciated

Please write a minimal working example. See link for more details what it means. // Please format your code. See How do I format code blocks? — user202729, Jan 23 '22 at 04:57
You inserted a line break \\ and an alignment marker & before both the a_n and b_n terms. Just remove those. (Of course, potentially what you wrote will not fit on one line.) — Willie Wong, Jan 23 '22 at 05:32
See also the explanation here: https://tex.stackexchange.com/a/424625/119 — Willie Wong, Jan 23 '22 at 05:35

score 4 · Answer 1 · edited Jan 23 '22 at 08:46

I'd like to suggest that you not use a split environment (or its close sibling, the aligned environment). Instead, I'd recommend you employ a multline* environment, especially since the integral expressions vary considerable in width, making it unappealing to employ an align* env.

The following screenshots shows solutions that employ a multline* and an align* environment. Note that I've tried to save some (horizontal) whitespace by a triple negative whitespace after all \int terms and changing \boxed{...} to `\boxed{!...!}.

\documentclass{article}
\usepackage[a4paper,margin=2.5cm]{geometry} % set page margins as needed
\usepackage{amsmath}
\begin{document}
\begin{multline*}
\int_{0}^{2\pi}! f(x)\cos(nx),dx 
   = \frac{1}{2}a_0!\int_{0}^{2\pi}!!!\cos(nx),dx\

a_1\boxed{!\int_{0}^{2\pi}!!!\cos(x)\cos(nx),dx!}
a_2 \boxed{!\int_{0}^{2\pi}!!!\cos(2x)\cos(nx),dx!}
\dots
a_n\boxed{!\int_{0}^{2\pi}!!!\cos^2(nx),dx!}  \
b_1\boxed{!\int_{0}^{2\pi}!!!\sin(x)\cos(nx),dx!}
b_2\boxed {!\int_{0}^{2\pi}!!!\sin(2x)\cos(nx),dx!}
\dots
b_n\boxed{!\int_{0}^{2\pi}!!!\sin(nx)\cos(nx),dx!}

\end{multline*}
\begin{align*}
\int_{0}^{2\pi}! f(x)&\cos(nx),dx 
  = \frac{1}{2}a_0!\int_{0}^{2\pi}!!!\cos(nx),dx\
 &+ a_1\boxed{!\int_{0}^{2\pi}!!!\cos(x)\cos(nx),dx!}

a_2 \boxed{!\int_{0}^{2\pi}!!!\cos(2x)\cos(nx),dx!}
\dots
a_n\boxed{!\int_{0}^{2\pi}!!!\cos^2(nx),dx!}  \

&+ b_1\boxed{!\int_{0}^{2\pi}!!!\sin(x)\cos(nx),dx!}

b_2\boxed {!\int_{0}^{2\pi}!!!\sin(2x)\cos(nx),dx!}
\dots
b_n\boxed{!\int_{0}^{2\pi}!!!\sin(nx)\cos(nx),dx!}

\end{align*}
\end{document}

score 3 · Accepted Answer · answered Jan 23 '22 at 10:44

You need some more generous text width, here obtained with geometry.

I'd emphasize the symmetries, using an alignedat enviroment to align the coefficients.

\documentclass{article}
\usepackage[a4paper]{geometry}
\usepackage{amsmath}
\newcommand{\diff}{\mathop{}!d}
\begin{document}
[
\newcommand{\rboxed}[1]{,\boxed{!#1!}}% local command
\begin{split}
&\int_{0}^{2\pi}f(x)\cos(nx)\diff x =\frac{a_0}{2}\int_{0}^{2\pi}\cos(nx)\diff x \
&\quad\begin{alignedat}[t]{7}
   &+a_1&&\rboxed{\int_{0}^{2\pi}\cos(x)\cos(nx)\diff x}
  &&+a_2&&\rboxed{\int_{0}^{2\pi}\cos(2x)\cos(nx)\diff x}
  &&+\dotsb
  &&+a_n&&\rboxed{\int_{0}^{2\pi}\cos(nx)\cos(nx)\diff x} \
   &+b_1&&\rboxed{\int_{0}^{2\pi}\sin(x)\cos(nx)\diff x}
  &&+b_2&&\rboxed{\int_{0}^{2\pi}\sin(2x)\cos(nx)\diff x}
  &&+\dotsb
  &&+b_n&&\rboxed{\int_{0}^{2\pi}\sin(nx)\cos(nx)\diff x}
  \end{alignedat}
\end{split}
]
\end{document}

We can improve by making the boxes into equal width by adding the difference in width between “sin” and “cos”:

\documentclass{article}
\usepackage[a4paper]{geometry}
\usepackage{amsmath}
\newcommand{\diff}{\mathop{}!d}
\begin{document}
[
\newcommand{\rboxed}[1]{,\boxed{!#1!}}% local command
\settowidth{\dimen8}{$\cos$}%
\settowidth{\dimen2}{$\sin$}%
\addtolength{\dimen8}{-\dimen2}%
\begin{split}
&\int_{0}^{2\pi}f(x)\cos(nx)\diff x =\frac{a_0}{2}\int_{0}^{2\pi}\cos(nx)\diff x \
&\quad\begin{alignedat}[t]{7}
   &+a_1&&\rboxed{\int_{0}^{2\pi}\cos(x)\cos(nx)\diff x}
  &&+a_2&&\rboxed{\int_{0}^{2\pi}\cos(2x)\cos(nx)\diff x}
  &&+\dotsb
  &&+a_n&&\rboxed{\int_{0}^{2\pi}\cos(nx)\cos(nx)\diff x} \
   &+b_1&&\rboxed{\int_{0}^{2\pi}\sin(x)\cos(nx)\diff x \kern\dimen8}
  &&+b_2&&\rboxed{\int_{0}^{2\pi}\sin(2x)\cos(nx)\diff x \kern\dimen8}
  &&+\dotsb
  &&+b_n&&\rboxed{\int_{0}^{2\pi}\sin(nx)\cos(nx)\diff x \kern\dimen8}
  \end{alignedat}
\end{split}
]
\end{document}

Arrange Equations

2 Answers2