展開する ((3ln(x)-5)^4)/x

解

展開する

\frac{( 3 ln ( x ) - 5 ) ^{4}}{x}

\frac{81 ln ^{4} ( x )}{x} - \frac{540 ln ^{3} ( x )}{x} + \frac{1350 ln ^{2} ( x )}{x} - \frac{1500 ln ( x )}{x} + \frac{625}{x}

解答ステップ

\frac{( 3 ln ( x ) - 5 ) ^{4}}{x}

(3 ln (x) - 5)^{4} = 81 ln^{4} (x) - 540 ln^{3} (x) + 1350 ln^{2} (x) - 1500 ln (x) + 625

= \frac{81 ln ^{4} ( x ) - 540 ln ^{3} ( x ) + 1350 ln ^{2} ( x ) - 1500 ln ( x ) + 625}{x}

分数の規則を適用する:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{81 ln ^{4} ( x ) - 540 ln ^{3} ( x ) + 1350 ln ^{2} ( x ) - 1500 ln ( x ) + 625}{x} = \frac{81 ln ^{4} ( x )}{x} - \frac{540 ln ^{3} ( x )}{x} + \frac{1350 ln ^{2} ( x )}{x} - \frac{1500 ln ( x )}{x} + \frac{625}{x}

= \frac{81 ln ^{4} ( x )}{x} - \frac{540 ln ^{3} ( x )}{x} + \frac{1350 ln ^{2} ( x )}{x} - \frac{1500 ln ( x )}{x} + \frac{625}{x}