Now, if anyone could change the title into something better that would be great =)
I am writing a rather long document, which contains plenty of integrals. I have a big list of integrals sorted in a three column style, as pictured below
The image is a tad old. Now, I want to link both the soutions and the answers to each question using hyperref. (Where the answer means just the antiderivate, and the solution means all the small steps to compute the integral) My problem is that I do not know what the best way to do this is. Right now, I have turned every integral into a hyperlink, as the MWE shows.
\documentclass[10pt,a4paper]{article}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{enumitem}
\usepackage{multicol}
\usepackage{mathtools}
\usepackage[english]{babel}
\usepackage{changepage}
\newcommand{\dx}{\mathop{}\! \text{d} x}
\newcommand{\R}{ \mathbb{R} }
\newcommand{\CC}{\mathcal{C}}
\newenvironment{IntList}[1]{%
\centering
\setlength{\columnsep}{50pt}
\begin{adjustwidth}{-3em}{-2em}\begin{multicols}{#1}\begin{enumerate}[itemsep=5pt]}{\end{enumerate}\end{multicols}\end{adjustwidth}}
\usepackage[hidelinks]{hyperref}
\hypersetup{
colorlinks=true, % false: boxed links; true: colored links
linkcolor=black, % color of internal links
citecolor=cyan, % color of links to bibliography
filecolor=magenta, % color of file links
urlcolor=cyan % color of external links
}
\newcommand{\IntExerc}[2]{\item \hyperref[#1]{\mbox{ \( \displaystyle #2 \) }}}
\begin{document}
\subsection{Huge ass list of problems}
\begin{IntList}{3}
\IntExerc{R1.1}{\int \frac{x^2+3x}{x^2} \dx }
\IntExerc{R1.22}{\int\sin(x)\,\mathrm{d}x}
\IntExerc{R1.2}{\int_0^1 \frac{x}{x^2+1} \dx}
\IntExerc{R1.3}{\int \frac{x}{x+1} \dx}
\IntExerc{R1.4}{\int_{-3}^{3} \frac{1}{1-x} \dx}
\IntExerc{R1.5}{\int \sqrt{4-x} \dx}
\IntExerc{R1.6}{\int_{0}^{1/2} \left( 2x - 1\right)^{50} \dx}
\IntExerc{R1.7}{\int \sqrt[n]{x} \dx}
\IntExerc{R1.8}{\int \frac{1}{x \ln x} \dx}
\IntExerc{R1.7}{\int \sin x \cos x \dx}
\IntExerc{R1.8}{\int_{1}^{\sqrt{e-1}} \ln\left( 1 + x^2 \right)x\dx}
\IntExerc{R1.9}{\int \frac{x}{e^x} \dx}
\IntExerc{R1.10}{\int \sin x \cos x \dx}
\IntExerc{R1.11}{\int_1^{e^n} \ln x \dx \ n \in \R}
\IntExerc{R1.12}{\int x \cdot a^x \dx}
\IntExerc{R1.13}{\int \log_{10} (x) \dx}
\IntExerc{R1.14}{\int_{\pi/6}^{\pi/3} \sin(x)^2 \dx}
\IntExerc{R1.15}{\int_1^e \int \frac{\pi}{-x^2} \dx \dx}
\IntExerc{R1.16}{\int_{0}^{\ln 2} x\ln(x+1) \dx}
\IntExerc{R1.17}{\int \frac{x e^x}{(x+1)^2} \dx}
\IntExerc{R1.18}{\int \frac{1}{1+\sqrt{x}}\dx}
\IntExerc{R1.19}{\int \frac{\ln x}{\sqrt{x}} \dx}
\IntExerc{R1.20}{\int_{\pi}^{\pi} \frac{\sin(1/x)e^{x^2}}{\sqrt{x!}} \dx}
\IntExerc{R1.21}{\int \frac{x-1}{\sqrt{x^2 + 2x + 7}} \dx}
\IntExerc{R1.22}{\int \frac{1 + e^x}{\sqrt{e^x + x}} \dx}
\IntExerc{R1.23}{\int \frac{e^x + 1}{e^x - 1} \dx}
\IntExerc{R1.24}{\int_{a}^{a+2\pi} \sin x+1 \dx}
\IntExerc{R1.25}{\int \frac{x^2 + 2x + 2}{x-1} \dx}
\IntExerc{R1.26}{\int_{0}^1 e^{-y^2} \dx}
\IntExerc{R1.30}{\int_{-3/4}^{4} \frac{x+1}{(x+2)^4}\dx}
\IntExerc{R1.27}{\int x^3\sqrt{1-x^2} \dx}
\IntExerc{R1.40}{\int \ln\left(\frac{1}{\sqrt{x}}\right) \dx}
\IntExerc{R1.28}{\int \sin(2x)e^{\sin(x)^2} \dx}
\IntExerc{R1.29}{\int x \ln \left( \frac{1}{x}\right) \dx}
\IntExerc{R1.30}{\int 2^x e^x \dx}
\IntExerc{R1.30}{\int \binom{x+1}{x} \dx}
\IntExerc{R1.31}{\int \frac{1}{\sqrt{x}\left( 1 + \sqrt{x}\right)} \dx}
\IntExerc{R1.32}{\int_{1}^{\log_e(a)^2} e^{\sqrt{x}}\dx}
\IntExerc{R1.33}{\int \frac{x^2}{x^2 - 1} \dx}
\IntExerc{R1.34}{\int \frac{x}{1 - x^2 + \sqrt{1 - x^2}} \dx}
\IntExerc{R1.34}{\int_{1}^{\sqrt{e-1}} \ln\left( 1 + x^2 \right)x\dx}
\IntExerc{R1.36}{\int \frac{x^2}{x^2 + 4x + 8}\dx}
\IntExerc{R1.37}{\int \frac{1}{x \ln(x)^n} \dx}
\IntExerc{R1.38}{\int_{0}^{\infty} x^3 e^{-x} \dx}
\IntExerc{R1.39}{\int e^{x + e^x} \dx}
\IntExerc{R1.40}{\int \ln(x)^3 \dx}
\IntExerc{R1.41}{\int \frac{x e^x}{\left( x + 1\right)^2}\dx}
\IntExerc{R1.42}{\int_n^m (m-x)(x-n)\dx}
\IntExerc{R1.41}{\int \frac{\pi}{\sqrt{e^2-16}}\dx}
\IntExerc{R1.40}{\int \frac{\sin(2x)}{\sin x} \dx}
\IntExerc{R1.40}{\int_0^{\pi/3n} \tan(nx) \dx}
\IntExerc{R1.40}{\int \frac{4a}{x^2-a^2} \dx}
\IntExerc{R1.40}{\int e^{\sin(x)^2}e^{\cos(x)^2} \dx}
\IntExerc{R1.40}{\int \frac{e^{\ln\left(x^2 + 1 \right)}}{x+1} \dx}
\IntExerc{R1.40}{\int_{\pi/6}^{\pi/2} \frac{1}{\tan x} \dx}
\IntExerc{R1.40}{\int \frac{x^2+1}{x(x^2+3)} \dx}
\IntExerc{R1.40}{\int \frac{1}{\sqrt[3]{x} + x} \dx}
\IntExerc{R1.40}{\int \frac{1}{x \ln x - x} \dx}
\IntExerc{R1.40}{\int_{0}^{\pi} \frac{x^2 \sin(x)}{\pi - 2} \dx}
\IntExerc{R1.40}{\int \sqrt{\sqrt{x} + \sqrt{x}\,} \dx}
\IntExerc{R1.40}{\int 2^{\ln x} \dx}
\IntExerc{R1.40}{\int_{2}^{5} \frac{2 - 4}{x^4 - x^2} \dx}
\IntExerc{R1.40}{\int \cos( \sin(x) ) \cos x \dx}
\IntExerc{R1.40}{\int \left(x + x^2\right)e^{3(x+\ln 3)} \dx}
\IntExerc{R1.40}{\int \cos(x)\sin(2x) \dx}
\IntExerc{R1.40}{\int \frac{1}{2x \sqrt{\ln x}} \dx}
\IntExerc{R1.40}{\int \frac{\log_5(x)}{\log_{25}(x)} \dx}
\end{IntList}
\subsubsection{Word problems}
$$ \int_{1/2}^{\sqrt{3}/2} \frac{x^3}{\left( \frac{5}{8} - x^4\right)\sqrt{\frac{5}{8} - x^4}}\quad $$
\newpage
\newpage
\begin{align}
\int \frac{x^2+3x}{x^2} \dx & = \int \frac{x^2}{x^2} + \frac{3x}{x^2} \dx = \int 1 \dx + 3\int \frac{dx}{x} = x + 3 \ln|x| + \CC \label{R1.1}\\
\int\sin(x)\,\mathrm{d}x & = -\cos(x) + C \label{R1.22} \\
\int\sin(x)\,\mathrm{d}x & = -\cos(x) + C \label{R1.40}
\end{align}
First straight integration problems, then word problems
\end{document}
Question(s): What is the best way to separate the plain answer, from the solution? (Are any of the ideas below good?)
- Can one perhaps add a spoiler tag (Opens on click)?
- Make the numbers into separate links?
- Add seperate links next to each integral? (I think this would make it very cluttered)
Oh, and is there any way to make the hyperref go both ways? That I could click on the answer, and get back to the questions?
Cheers, thanks in advance for any suggestions, answers or comments =)
