積分(3)の1．(3)のヒント

分子を有理化の計算

$3$\displaystyle{\begin{array}{lll}\frac{\hspace{2}1\hspace{2}}{\hspace{2} \sqrt{ 2x+1 }+\sqrt{ 2x } \hspace{2}}& \vspace{6}\\ =\frac{\hspace{2} \sqrt{ 2x+1 }- \sqrt{ 2x } \hspace{2}}{\hspace{2} $ \sqrt{ 2x+1 }+\sqrt{ 2x } $ $ \sqrt{ 2x+1 }- \sqrt{ 2x } $ \hspace{2}}& \vspace{6}\\ =\frac{\hspace{2} \sqrt{ 2x+1 }- \sqrt{ 2x } \hspace{2}}{\hspace{2} { $ \sqrt{ 2x+1 } $ }^{2}- { $ \sqrt{ 2x } $ }^{2} \hspace{2}}& \vspace{6}\\ =\frac{\hspace{2} \sqrt{ 2x+1 }- \sqrt{ 2x } \hspace{2}}{\hspace{2} 2x+1- 2x \hspace{2}}& \vspace{6}\\ =\frac{\hspace{2} \sqrt{ 2x+1 }- \sqrt{ 2x } \hspace{2}}{\hspace{2}1\hspace{2}}& \vspace{6}\\ =\sqrt{ 2x+1 }- \sqrt{ 2x }& \vspace{6}\\ \end{array}}$

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