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% Document Info
\author{CROSSANT (CROSSANT)}
\pdfinfo{
  /Title (integral-cases-for-trigonometric-powers.pdf)
  /Creator (Cheatography)
  /Author (CROSSANT (CROSSANT))
  /Subject (Integral Cases for Trigonometric Powers Cheat Sheet)
}

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\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
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    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Integral Cases for Trigonometric Powers Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{CROSSANT (CROSSANT)} via \textcolor{DarkBackground}{\uline{cheatography.com/186482/cs/43796/}}}
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  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}CROSSANT (CROSSANT) \\
  \uline{cheatography.com/crossant} \\
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  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Published 6th July, 2024.\\
   Updated 18th December, 2024.\\
   Page {\thepage} of \pageref{LastPage}.
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  Measure your website readability!\\
  www.readability-score.com
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\begin{document}
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\begin{multicols*}{2}

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% Row 0
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\mymulticolumn{1}{x{8.4cm}}{{\bf{Case Name}}} \tn 
% Row Count 1 (+ 1)
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% Row Count 3 (+ 1)
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\par\addvspace{1.3em}

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\mymulticolumn{1}{x{8.4cm}}{Sine-Even and Cosine-Even} \tn 
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\mymulticolumn{1}{x{8.4cm}}{Sine-Cosine Same} \tn 
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\begin{tabularx}{8.4cm}{x{4.72 cm} x{3.28 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Pythagorean Identities}}  \tn
% Row 0
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Sine Pythagorean & sin\textasciicircum{}2\textasciicircum{}(x)=1-cos\textasciicircum{}2\textasciicircum{}(x) \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
Cosine Pythagorean & cos\textasciicircum{}2\textasciicircum{}(x)=1-sin\textasciicircum{}2\textasciicircum{}(x) \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
Tangent Pythagorean & tan\textasciicircum{}2\textasciicircum{}(x)=sec\textasciicircum{}2\textasciicircum{}(x)-1 \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
Cosecant Pythagorean & csc\textasciicircum{}2\textasciicircum{}(x)=cot\textasciicircum{}2\textasciicircum{}(x)+1 \tn 
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% Row 4
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Secant Pythagorean & sec\textasciicircum{}2\textasciicircum{}(x)=tan\textasciicircum{}2\textasciicircum{}(x)+1 \tn 
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% Row 5
\SetRowColor{white}
Cotangent Pythagorean & cot\textasciicircum{}2\textasciicircum{}(x)=csc\textasciicircum{}2\textasciicircum{}(x)-1 \tn 
% Row Count 12 (+ 2)
% Row 6
\SetRowColor{LightBackground}
Sine-Cosine Pythagorean & 1=sin\textasciicircum{}2\textasciicircum{}(x)+cos\textasciicircum{}2\textasciicircum{}(x) \tn 
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% Row 7
\SetRowColor{white}
Secant-Tangent Pythagorean & 1=sec\textasciicircum{}2\textasciicircum{}(x)-tan\textasciicircum{}2\textasciicircum{}(x) \tn 
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% Row 8
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Cosecant-Cotangent Pythagorean & 1=csc\textasciicircum{}2\textasciicircum{}(x)-cot\textasciicircum{}2\textasciicircum{}(x) \tn 
% Row Count 18 (+ 2)
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\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Reduction Formulas}}  \tn
% Row 0
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∫sin\textasciicircum{}n\textasciicircum{}(x)dx, {\emph{n≥2}} & -cos(x)sin\textasciicircum{}n-1\textasciicircum{}(x)/n + (n-1/n)∫sin\textasciicircum{}n-2\textasciicircum{}(x)dx \tn 
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% Row 1
\SetRowColor{white}
∫cos\textasciicircum{}n\textasciicircum{}(x)dx, {\emph{n≥2}} & cos(x)\textasciicircum{}n-1\textasciicircum{}sin(x)/n + (n-1/n)∫cos\textasciicircum{}n-2\textasciicircum{}(x)dx \tn 
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% Row 2
\SetRowColor{LightBackground}
∫tan\textasciicircum{}n\textasciicircum{}(x)dx, {\emph{n≥2}} & tan\textasciicircum{}n-1\textasciicircum{}(x)/(n-1) - ∫tan\textasciicircum{}n-2\textasciicircum{}(x)dx \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
∫csc\textasciicircum{}n\textasciicircum{}(x)dx, {\emph{n≥2}} & -csc\textasciicircum{}n-2\textasciicircum{}(x)cot(x)/(n-1) + ((n-2)/(n-1))∫csc\textasciicircum{}n-2\textasciicircum{}(x)dx \tn 
% Row Count 9 (+ 3)
% Row 4
\SetRowColor{LightBackground}
∫sec\textasciicircum{}n\textasciicircum{}(x)dx, {\emph{n≥2}} & sec\textasciicircum{}n-2\textasciicircum{}(x)tan(x)/(n-1) + ((n-2)/(n-1))∫sec\textasciicircum{}n-2\textasciicircum{}(x)dx \tn 
% Row Count 12 (+ 3)
% Row 5
\SetRowColor{white}
∫cot\textasciicircum{}n\textasciicircum{}(x)dx, {\emph{n≥2}} & -cot\textasciicircum{}n-1\textasciicircum{}(x)/(n-1) - ∫cot\textasciicircum{}n-2\textasciicircum{}(x)dx \tn 
% Row Count 14 (+ 2)
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\mymulticolumn{2}{x{8.4cm}}{n ∈ ℕ\textasciitilde{}1\textasciitilde{} = \{1,2,3,4,5,...\}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{8.4cm}{x{4 cm} x{4 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{2}{x{8.4cm}}{\bf\textcolor{white}{Miscellaneous Information}}  \tn
% Row 0
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Binomial Expansion & (a+b)\textasciicircum{}n\textasciicircum{} = ∑\textasciicircum{}n\textasciicircum{}\textasciitilde{}k=0\textasciitilde{} (\textasciicircum{}n\textasciicircum{}\textasciitilde{}k\textasciitilde{}) a\textasciicircum{}n-k\textasciicircum{}b\textasciicircum{}k\textasciicircum{} \tn 
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% Row 1
\SetRowColor{white}
Integral Linearity Property: Sum and Difference & ∫(f(x) ± g(x))dx = ∫f(x)dx ± ∫g(x)dx \tn 
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% Row 2
\SetRowColor{LightBackground}
∫tan(x)dx & ln|sec(x)|+C \tn 
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% Row 3
\SetRowColor{white}
∫cot(x)dx & ln|sin(x)|+C \tn 
% Row Count 8 (+ 1)
% Row 4
\SetRowColor{LightBackground}
∫sec(x)dx & ln|sec(x)+tan(x)|+C \tn 
% Row Count 9 (+ 1)
% Row 5
\SetRowColor{white}
∫sec\textasciicircum{}3\textasciicircum{}(x)dx & $\frac{1}{2}$(sec(x)tan(x)+ln|sec(x)+tan(x)|)+C \tn 
% Row Count 13 (+ 4)
% Row 6
\SetRowColor{LightBackground}
∫csc(x)dx & ln|csc(x)-cot(x)|+C \tn 
% Row Count 14 (+ 1)
% Row 7
\SetRowColor{white}
∫csc\textasciicircum{}3\textasciicircum{}(x)dx & -$\frac{1}{2}$(csc(x)cot(x)+ln|csc(x)+cot(x)|)+C \tn 
% Row Count 18 (+ 4)
\hhline{>{\arrayrulecolor{DarkBackground}}--}
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\mymulticolumn{2}{x{8.4cm}}{(\textasciicircum{}n\textasciicircum{}\textasciitilde{}k\textasciitilde{}) are the binomial coefficients, equal to n!/(k!(n-k)!) \newline n, k ∈ ℕ\textasciitilde{}1\textasciitilde{} = \{1,2,3,4,5,...\}}  \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}--}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}