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Math Help - Integration using partial fractions

1. Integration using partial fractions

S 1/[(t+4)(t-1)]dt is my problem. I'm having trouble understanding how to use the '1' here.

Thanks!

2. Originally Posted by JYZero
S 1/[(t+4)(t-1)]dt is my problem. I'm having trouble understanding how to use the '1' here.

Thanks!
Let $\frac{A}{t + 4} + \frac{B}{t - 1} = \frac{1}{(t + 4)(t - 1)}$

$\frac{A(t - 1) + B(t + 4)}{(t + 4)(t - 1)} = \frac{1}{(t + 4)(t - 1)}$

$A(t - 1) + B(t + 4) = 1$

$At - A + Bt + 4B = 1$

$(A + B)t + 4B - A = 0t + 1$.

So $A + B = 0$ and $4B - A = 1$

$4B - 1 = A$

So $4B - 1 + B = 0$

$5B - 1 = 0$

$B = \frac{1}{5}$

$A + B = 0$

$A + \frac{1}{5} = 0$

$A = -\frac{1}{5}$.

So $\int{\frac{1}{(t + 4)(t - 1)}\,dt} = \int{-\frac{1}{5}\left(\frac{1}{t + 4}\right) + \frac{1}{5}\left(\frac{1}{t - 1}\right)\,dt}$

$= \frac{1}{5}\int{\frac{1}{t - 1} - \frac{1}{t + 4}\,dt}$

$= \frac{1}{5}\left[\ln{|t - 1|} - \ln{|t + 4|}\right] + C$

$= \frac{1}{5}\ln{\left|\frac{t - 1}{t + 4}\right|} + C$.

3. Originally Posted by JYZero
S 1/[(t+4)(t-1)]dt is my problem. I'm having trouble understanding how to use the '1' here.
$\frac{1}{(t+4)(t-1)}=\frac{1}{5}\cdot \frac{(t+4)-(t-1)}{(t+4)(t-1)}=\frac{1}{5}\left( \frac{1}{t-1}-\frac{1}{t+4} \right).$

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# Removing the indent of the first paragraph of a section (in French language)

I want to remove the indent just for the first paragraph of a section. I am looking for an automatic solution. (I mean, it should be invisible for the "user", who does not have to type no indent)

I have tried

\documentclass{article}
\usepackage[french]{babel}
\usepackage{lipsum}

\newcommand{\mySection}[1]{\section*{#1}\noindent}

\begin{document}
\mySection{Test}
\lipsum[1]
\end{document}

But it does not work. There is a single space at the very beginning of the paragraph.

• Why is it so?
• And how can I achieve this?
• Only from the first paragraph? Or all? Mar 19, 2016 at 19:47
• Only the first one. Mar 19, 2016 at 19:48
• @Alenanno, nope, \usepackage{indentfirst} does just the opposite. Mar 19, 2016 at 19:52
• @Colas If the package can set it to true, it can be set to false. See tex.stackexchange.com/q/132369/4778 Mar 19, 2016 at 19:54
• if you start the paragraph prematurely with \noindent then the end of line following the heading will make a space unless you comment it out, also a blank line following the heading, which is normally correct markup would make a spurious paragraph. Mar 19, 2016 at 20:44

Add \frenchbsetup{IndentFirst=false} to your preamble (p. 6 of the documentation):

\documentclass{article}
\usepackage[french]{babel}
\usepackage{lipsum}

\frenchbsetup{IndentFirst=false}

\begin{document}

\section{Zzzzz}
\lipsum[1]
\end{document}

• Thanks @David Carlisle, for your patience with my typos… Mar 19, 2016 at 20:55
• I love your sleepy sections! Mar 19, 2016 at 21:02
• mainly just clarifying that it worked with normal \section no need for user \Section wrapper. Mar 19, 2016 at 21:12