RUMUS DASAR
| \(\int \sin x \: dx\) | \(- \cos x + c\) |
| \(\int \cos x \: dx\) | \(\sin x + c\) |
| \(\int \tan x \: dx\) | \(\ln | \sec x | + c\) |
| \(\int \cot x \: dx\) | \(\ln | \sin x | + c\) |
| \(\int \sec x \: dx\) | \(\ln | \sec x + \tan x | + c\) |
| \(\int \csc x \: dx\) | \(\ln | \csc x - \cot x | + c\) |
| \(\int \sec^2 x \: dx\) | \(\tan x + c\) |
| \(\int \csc^2 x \: dx\) | \(\cot x + c\) |
| \(\int \sec x \tan x \: dx\) | \(\sec x + c\) |
| \(\int \csc x \cot x \: dx\) | \(- \csc x + c\) |
Contoh 01
\begin{equation*} \begin{split} & \int \sin(3x+2)\:dx \\\\ & \int \sin(3x+2)\:\frac{d(3x+2)}{3} \\\\ & \frac{1}{3}\int \sin(3x+2)\:d(3x+2) \\\\ & \bbox[5px, border: 2px solid magenta] {-\frac{1}{3}\cos(3x+2)+ c} \end{split} \end{equation*}
Contoh 02
\begin{equation*} \begin{split} & \int \cos(1-2x)\:dx\\\\ & \int \cos(1-2x)\:\frac{d(1-2x)}{-2}\\\\ & -\frac{1}{2}\int \cos(1-2x)\:d(1-2x)\\\\ & \bbox[5px, border: 2px solid magenta] {-\frac{1}{2}\sin(1-2x)+ c} \end{split} \end{equation*}
Contoh 03
\begin{equation*} \begin{split} & \int \tan(2x + 1)\:dx\\\\ & \int \tan(2x + 1)\:\frac{d(2x + 1)}{2}\\\\ & \frac{1}{2}\int \tan(2x + 1)\:d(2x + 1)\\\\ & \bbox[5px, border: 2px solid magenta] {\frac{1}{2} \ln|\sec (2x + 1) | + c} \end{split} \end{equation*}
SOAL LATIHAN