$3$\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{C}$ は積分定数

$3$\displaystyle{{x}^{{\alpha}}}$ の微分を参照のこと。

■計算例
$3$\displaystyle{\displaystyle{ \int {x}^{2}dx }=\frac{\hspace{2}1\hspace{2}}{\hspace{2}3\hspace{2}}{x}^{3}+C}$

■応用公式
$3$\displaystyle{\begin{array}{lll}\displaystyle{ \int { $ ax+b $ }^{{\alpha}}dx }& \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2}a\hspace{2}}\cdot \frac{\hspace{2}1\hspace{2}}{\hspace{2} {\alpha}+1 \hspace{2}}{ $ ax+b $ }^{ {\alpha}+1 }+C& \vspace{6}\\ \end{array}}$
　 $3$\displaystyle{a}$ ， $3$\displaystyle{b}$ は定数

■計算例
$3$\displaystyle{\begin{array}{lll}\displaystyle{ \int { $ 4x+3 $ }^{5}dx }& \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2}4\hspace{2}}\cdot \frac{\hspace{2}1\hspace{2}}{\hspace{2}6\hspace{2}}{ $ 4x+3 $ }^{6}+C& \vspace{6}\\ =\frac{\hspace{2}1\hspace{2}}{\hspace{2} 24 \hspace{2}}{ $ 4x+3 $ }^{6}+C& \vspace{6}\\ \end{array}}$