# Integral Aljabar

### Bentuk dasar

###### Bentuk Dasar

$$\int x^n \: dx = \dfrac {1}{n + 1} \:.\: x^{n + 1} + c$$

$$\int x^{-1} \: dx = \ln |x| + c$$

$$\int k \: dx = kx + c$$, k adalah konstanta

Contoh 01

\begin{equation*} \begin{split} \int x^4 \: dx & = \frac {1}{4 + 1} \:.\: x^{4 + 1} + c \\\\ \int x^4 \: dx & = \frac {1}{5} x^{5} + c \end{split} \end{equation*}

Contoh 02

\begin{equation*} \begin{split} \int 3x^8 \: dx & = 3 \:.\: \frac {1}{8 + 1} \:.\: x^{8 + 1} + c \\\\ \int 3x^8 \: dx & = \frac {1}{3} x^{9} + c \end{split} \end{equation*}

Contoh 03

\begin{equation*} \begin{split} \int \sqrt{x} \: dx & = \int x^{\frac 12} \: dx \\\\ \int \sqrt{x} \: dx & = \frac {1}{\frac 12 + 1} \:.\: x^{\frac 12 + 1} + c \\\\ \int \sqrt{x} \: dx & = \frac {1}{\frac 32} \:.\: x^{\frac 12 + 1} + c \\\\ \int \sqrt{x} \: dx & = \frac {2}{3} x^{1 \frac 12} + c \\\\ \int \sqrt{x} \: dx & = \frac {2}{3} x \sqrt{x} + c \end{split} \end{equation*}

Contoh 04

\begin{equation*} \begin{split} \int \frac {1}{x^3} \: dx & = \int x^{-3} \: dx \\\\ \int \frac {1}{x^3} \: dx & = \frac {1}{-3 + 1} \:.\: x^{-3 + 1} + c \\\\ \int \frac {1}{x^3} \: dx & = -\frac {1}{2} x^{-2} + c \\\\ \int \frac {1}{x^3} \: dx & = -\frac {1}{2 x^2} + c \end{split} \end{equation*}

Contoh 05

\begin{equation*} \begin{split} \int \frac 2x \: dx & = 2 \int \frac 1x \: dx \\\\ \int \frac 2x \: dx & = 2 \ln |x| + c \end{split} \end{equation*}

Contoh 06

\begin{equation*} \begin{split} \int 4 \: dx & = 4x + c \end{split} \end{equation*}

##### SOAL LATIHAN

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