積分の公式

$3$\displaystyle{C}$ は積分定数である。

$3$\displaystyle{ \displaystyle{ \int {x}^{{\alpha}}dx }=\frac{\hspace{2}1\hspace{2}}{\hspace{2} {\alpha}+1 \hspace{2}}{x}^{ {\alpha}+1 }+C }$
（ $3${\alpha}$ は－1以外の実数）⇒
$3$\displaystyle{\displaystyle{ \int {e}^{x}dx }={e}^{x}+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2}x\hspace{2}}dx }=\log \|x\| +C}$
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$3$\displaystyle{\displaystyle{ \int {a}^{x}dx }=\frac{\hspace{2} {a}^{x} \hspace{2}}{\hspace{2} \log a \hspace{2}}+C}$
　( $3$\displaystyle{a}$ は0より大きい定数)⇒
$3$\displaystyle{\displaystyle{ \int \sin xdx }=- \cos x+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \cos xdx }=\sin x+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \cos }^{2}x \hspace{2}}dx }=\tan x+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} { \sin }^{2}x \hspace{2}}dx }=- \frac{\hspace{2}1\hspace{2}}{\hspace{2} \tan x \hspace{2}}+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ 1- {x}^{2} } \hspace{2}}dx }={\sin }^{ - 1 }x+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} 1+{x}^{2} \hspace{2}}dx }={\tan }^{ - 1 }x+C}$
　⇒
$3$\displaystyle{\displaystyle{ \int \frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ {x}^{2}+A } \hspace{2}}dx }}$
　 $3$\displaystyle{=\log \| x+\sqrt{ {x}^{2}+A } \| +C}$
　( $3$\displaystyle{A}$ は任意定数)⇒