Math

Basics

To render any math equation, the math equation must be between <math></math> i.e., <math>f(x)=x^2</math> gives $f(x)=x^{2}$.

Common math commands

Superscript & Subscript

Superscript: <math>x^{5+y}</math> gives $x^{5+y}$
Subscript: <math>x_{5+t}</math> gives $x_{5+t}$
Together: <math>x_{5+t}^{5+y}</math> gives $x_{5+t}^{5+y}$

Fractions, radicals and brackets

Fractions: <math>\frac{1}{x}</math> gives ${\frac {1}{x}}$
Bad brackets, parentheses, etc.: <math>(\frac{1}{x})^3</math> gives $({\frac {1}{x}})^{3}$
Correct brackets, parentheses, etc.: <math>\left(\frac{1}{x}\right)^3</math> gives $\left({\frac {1}{x}}\right)^{3}$
Square root: <math>\sqrt{x+1}</math> gives ${\sqrt {x+1}}$
General radical: <math>\sqrt[3]{64}=4</math> gives ${\sqrt[{3}]{64}}=4$

Trig. & Log Functions

Sin, cos, tan, etc.: <math>\sin{(\theta)}</math> gives $\sin {(\theta )}$
Arcsin, arccos, arctan, etc.: <math>\arcsin{(\theta)}</math> gives $\arcsin {(\theta )}$
Log: <math>\log_{5}{5^2}=2</math> gives $\log _{5}{5^{2}}=2$
Ln: <math>\ln{e^3}=3</math> gives $\ln {e^{3}}=3$

Calculus

Sum: <math>\sum_{i=1}^{n}i=\frac{n(n+1)}{2}</math> gives $\sum _{i=1}^{n}i={\frac {n(n+1)}{2}}$

Limit: <math>\lim_{h\to 0}\frac{f(x+h)-f(x)}{h}</math> gives $\lim _{h\to 0}{\frac {f(x+h)-f(x)}{h}}$

Derivative: <math>\frac{d}{dx}\left[\frac{1}{x}\right]=-\frac{1}{x^2}</math> gives ${\frac {d}{dx}}\left[{\frac {1}{x}}\right]=-{\frac {1}{x^{2}}}$

Integral: <math>\int_{1}^{x+1}\frac{1}{r}dr</math> gives $\int _{1}^{x+1}{\frac {1}{r}}dr$

Limit bar: <math>\bigg|_{0}^{1}</math> gives ${\bigg |}_{0}^{1}$

Advanced

Sometimes it might be necessary to break up and align a long equation such as:

${\begin{aligned}\int _{0}^{1}\left(3+x{\sqrt {x}}\right)dx&=\int _{0}^{1}\left(3+x^{1}{x}^{\frac {1}{2}}\right)dx=\int _{0}^{1}\left(3+x^{1+{\frac {1}{2}}}\right)dx=\int _{0}^{1}\left(3+x^{\frac {3}{2}}\right)dx\\[2ex]&=3x+{\frac {x^{{\frac {3}{2}}+1}}{{\frac {3}{2}}+1}}{\bigg |}_{0}^{1}=3x+{\frac {x^{\tfrac {5}{2}}}{\frac {5}{2}}}{\bigg |}_{0}^{1}=3x+{\frac {2x^{\frac {5}{2}}}{5}}{\bigg |}_{0}^{1}\\[2ex]&=\left[3(1)+{\frac {2(1)^{5/2}}{5}}\right]-\left[3(0)+{\frac {2(0)^{5/2}}{5}}\right]\\[2ex]&=3+{\frac {2}{5}}={\frac {15}{5}}+{\frac {2}{5}}={\frac {17}{5}}\end{aligned}}$

To do this use &= where the equation = should align and put \begin{align} and \end{align} at the start and end of <math></math>. Finally use \\[2ex] to create the proper space between the lines (if they're too close) and to push the rest of the equation to the next line. The code below renders what is seen above:

<math>
\begin{align}

\int_{0}^{1}\left(3+x\sqrt{x}\right)dx &= \int_{0}^{1}\left(3+x^{1}{x}^{\frac{1}{2}}\right)dx = \int_{0}^{1}\left(3+x^{1+\frac{1}{2}}\right)dx  = \int_{0}^{1}\left(3+x^{\frac{3}{2}}\right)dx \\[2ex]

&= 3x+\frac{x^{\frac{3}{2}+1}}{\frac{3}{2}+1}\bigg|_{0}^{1} = 3x+\frac{x^{\tfrac{5}{2}}}{\frac{5}{2}}\bigg|_{0}^{1} = 3x+\frac{2x^{\frac{5}{2}}}{5}\bigg|_{0}^{1} \\[2ex]

&= \left[3(1)+\frac{2(1)^{5/2}}{5}\right]-\left[3(0)+\frac{2(0)^{5/2}}{5}\right] \\[2ex]

&= 3+\frac{2}{5} = \frac{15}{5}+\frac{2}{5} = \frac{17}{5}  

\end{align}
</math>