$\frac{\left(2x+1\right)^5}{10}+C$  

 $\frac{\left(2x+1\right)^5}{2}+C$  

 $\left(2x+1\right)^5+C$  

 $\ln x+C$  

 $\ln3x+C$  

 $3\ln x+c$  

 $\frac{1}{3}\ln x+c$  

 $x^0+c$  

 $\ln x+c$  

 $x^{-1}+C$  

 $\frac{1}{x^2}+c$  

 $\frac{e^{5y}}{5}+C$  

 $5e^{5y}+C$  

 $e^{5y}+C$  

 $\frac{e^{5y+1}}{5}+C$  

 $\frac{\ln\left|4x-3\right|}{2}+c$  

 $\frac{\ln\left|4x-3\right|}{4}+c$  

 $2\ln\left|4x-3\right|+c$  

 $\frac{\left(2-x\right)^{-2}}{2}+c$  

 $\frac{\left(2-x\right)^{-2}}{-2}+c$  

 $\frac{\ln\left|2-3x\right|^{-2}}{-2}+C$  

 $\frac{\left(2-x\right)^4}{-4}+c$  

 $-e^{\left(2-3x\right)}+C$  

 $3e^{\left(2-3x\right)}+C$  

 $\ln e^{\left(2-3x\right)}+C$  

Substitution Method

By parts

Basic Rule log

 $3\ln\left|x\right|+C$  

 $3$  

 $\frac{3}{x^2}+C$  

 $\frac{e^{1-4x}}{-4}+C$  

 $-4e^{1-4x}$  

Substitution Method

Basic Rule

By Parts 

By parts

Substitution Method

double angle

by parts

substitution method

double angle

product rule

 $\left(x-h\right)^2=4p\left(y-k\right)$  

 $\left(y-k\right)^2=4p\left(x-h\right)$  

 $\left(x-h\right)^2=4p\left(y-k\right)\$  

 $\left(y-k\right)^2=4p\left(x-h\right)$  

 $c^2=a^2-b^2$  

 $c^2=b^2-a^2$  

 $x=2-4t$  ; $y=-5+2t$  ; $z=-3+4t$  

 $\frac{x-2}{-4}=\frac{y+5}{2}=\frac{z+3}{1}$  

 $x=-4+2t$  ; $y=2-5t$  ; $z=1-3t$  

$\cos\theta=\frac{a\times b}{\left|a\right|\left|b\right|}$

$\sin\theta=\frac{a\cdot b}{\left|a\right|\left|b\right|}$

$\cos\theta=\frac{a\cdot b}{\left|a\right|\left|b\right|}$

 $6\times0\times2$  

 $6+0+2$  

 $2+6-1+3-2$  

 $\left|\overrightarrow{AB}\times\overrightarrow{AC}\right|$  

 $\frac{1}{2}\left|\overrightarrow{AB}\times\overrightarrow{AC}\right|$  

 $\frac{1}{2}\left|\overrightarrow{AB}\times\overrightarrow{BC}\right|$  

 $\cos\theta=\frac{a_1\cdot a_2}{\left|a_1\right|\left|a_2\right|}$  

 $\cos\theta=\frac{n_1\cdot n_2}{\left|n_1\right|\left|n_2\right|}$  

 $\sin\theta=\frac{n_1\cdot n_2}{\left|n_1\right|\left|n_2\right|}$  

 $50$  

 $\sqrt{50}=5\sqrt{2}$  

 $12$  

 $unit\ vector\ ,\ v-w=\frac{v-w}{\left|v-w\right|}$  

 $unit\ vector\ ,\ v-w=\frac{v-w}{\left|v\right|\left|w\right|}$  

 $unit\ vector\ ,\ v-w=\frac{\left|v-w\right|}{v-w}$  

$x_{n+1}=x_n-\frac{f'\left(x_n\right)}{f\left(x_n\right)}$

$x_{n+1}=x_n+\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

$x_{n+1}=x_n-\frac{f\left(x_n\right)}{f'\left(x_n\right)}$

 $h=\frac{\pi-0}{6}$  ;  mode degree ; value in table is 5 d.p.

 $h=\frac{\pi-0}{5}$  ; mode must in radian ; value in table 5 d.p.

standard form :  $\frac{\text{d}x}{\text{d}y}+\frac{3}{x}y=x$  

 $IF\ =\ e^{\int\frac{3}{x}dx}$  

 $xdy+3y=x^2dx$  

$\frac{1}{x}$

$e^x$

$\ln x$

$e^x$

$-e^x$

$\ln x$

 $b^2-4ac$  

 $\left(x-h\right)^2+\left(y-k\right)^2=r^2$  

A parallel vector

A perpendicular vector

A point on the line

A parallel vector to the line and a point on the line

An orthogonal vector

A normal vector to the plane

A point on the plane

An orthogonal/ perpendicular vector to the plane and a point on the plane

Symmetric equation

Parametric equation

Vector component form

Point normal form

 $\sqrt{3^2+2^2+\left(-4^2\right)}$  

 $3^2+2^2+\left(-4\right)^2$  

 $4\left(x-1\right)^2+\left(y-2\right)^2=1$  ; $C\left(1,2\right)$  ; $V\left(-1,2\right)\ \&\ \left(3,2\right)$  

 $\frac{\left(x-1\right)^2}{1}+\frac{\left(y-2\right)^2}{4}=1$  ;  $C\left(1,2\right)$ ; $V\left(1,4\right)\ \&\ \left(1,0\right)$  

 $\frac{\left(x-4\right)^2}{3}+\frac{\left(y-2\right)^2}{12}=1$  ; $C\left(4,2\right)$  ;  $V\left(4,2\pm2\sqrt{3}\right)$