İntegral Alma Kuralları Nelerdir?

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İntegral nasıl alınır? Maddeler halinde integral alma kuralları, integral formülleri, açıklamaları

İntegral Alma Kuralları;

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\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

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\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

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\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

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