İntegral Alma Kuralları Nelerdir?

İntegral Alma Kuralları;

$\displaystyle 1)\int{dx=x+C}$

$\displaystyle 2)\int{\alpha dx=\alpha \int{dx=}}\alpha x+C$ (α bir sabit)

$\displaystyle 3)\int{{{x}^{n}}}dx=\frac{{{x}^{n+1}}}{n+1}+C$ (n ≠ -1)

$\displaystyle 4)\int{\frac{{{f}^{'}}(x)}{f(x)}}dx=\ln \left| f\left( x \right) \right|+C$

$\displaystyle 5)\int{\frac{1}{x}}dx=\ln \left| x \right|+C$

$\displaystyle 6)\int{{{e}^{u\left( x \right)}}}.{{u}^{'}}\left( x \right)dx={{e}^{u\left( x \right)}}+C$

$\displaystyle 7)\int{{{e}^{x}}}dx={{e}^{x}}+C$

$\displaystyle 8)\int{{{a}^{u\left( x \right)}}}.{{u}^{'}}\left( x \right)dx=\frac{{{a}^{u(x)}}}{\ln a}+C$

$\displaystyle 9)\int{{{a}^{x}}}dx=\frac{{{a}^{x}}}{\ln a}+C$

$\displaystyle 10)\int{Sinxdx}=-Cosx+C$

$\displaystyle 11)\int{Cosxdx=Sinx+C}$

$\displaystyle 12)\int{Se{{c}^{2}}}xdx=\int{\left( 1+Ta{{n}^{2}}x \right)}dx=\int{\frac{1}{Co{{s}^{2}}x}}dx=Tanx+C$

$\displaystyle 13)\int{Co{{\sec }^{2}}}xdx=\int{\left( 1+Co{{t}^{2}}x \right)}dx=\int{\frac{1}{Si{{n}^{2}}x}}dx=-Cotx+C$

$\displaystyle 14)\int{\frac{1}{\sqrt{1-{{x}^{2}}}}}dx=ArcSinx+C$

$\displaystyle 15)\int{\frac{-1}{\sqrt{1-{{x}^{2}}}}}dx=ArcCosx+C$

$\displaystyle 16)\int{\frac{1}{1+{{x}^{2}}}}dx=ArcTanx+C$

$\displaystyle 17)\int{\frac{-1}{1+{{x}^{2}}}}dx=ArcCotx+C$

$\displaystyle 18)\int{Sin\left( ax+b \right)}dx=-\frac{1}{a}Cos\left( ax+b \right)+C$

$\displaystyle 19)\int{Cos\left( ax+b \right)}dx=-\frac{1}{a}Sin\left( ax+b \right)+C$

$\displaystyle 20)\int{\frac{1}{Si{{n}^{2}}\left( ax+b \right)}}dx=-\frac{1}{a}Cot\left( ax+b \right)+C$

$\displaystyle 21)\int{\frac{1}{Co{{s}^{2}}\left( ax+b \right)}}dx=-\frac{1}{a}Tan\left( ax+b \right)+C$

Permütasyon ve Kombinezon (Kombinasyon) Hesaplamaları Nasıl Olur?