Further maths Pure

$re^{i\theta}$

$\frac{e^{i\theta}+e^{-i\theta}}{2}$

$\frac{e^{i\theta}-e^{-i\theta}}{2}$

$z^n=r^n(\cos n\theta+i\sin n\theta)$

For the value for which the integrand is undefined, substitute the value for a variable and consider the value of the integral as that variable tends to the original value

$\mathcal{\overline{f(x)}=\frac{1}{b-a}\int_{a}^{b} f(x).dx}$

${\frac{A}{\mathcal{x-a}}+\frac{B\mathcal{x}+C}{\mathcal{x^2+bx+c}}}$

$\mathcal{\frac{(ax+b)^{n+1}}{a(n+1)}+c}$

$\mathcal{\frac{e^{ax+b}}{a}+c}$

$\mathcal{\frac{1}{a}\ln{|ax+b|}+c}$

$\mathcal{\frac{e^x+e^{-x}}{2}}$

$\mathcal{\frac{e^x-e^{-x}}{2}}$

$\mathcal{\frac{e^x-e^{-x}}{e^x+e^{-x}}}$