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

Fractions: <math>\frac{1}{x}</math> gives ${\frac {1}{x}}$
Square root: <math>\sqrt{x+1}</math> gives ${\sqrt {x+1}}$
General Radical: <math>$\sqrt[3]{64}=4</math> gives ${\sqrt[{3}]{64}}=4$

---

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

123${\displaystyle }$