展开 (e^{-6x}(e^{6x}-1)^2)/4+1

解答

展开

\frac{e ^{- 6 x} ( e ^{6 x} - 1 ) ^{2}}{4} + 1

\frac{e ^{6 x}}{4} - \frac{1}{2} + \frac{e ^{- 6 x}}{4} + 1

求解步骤

\frac{e ^{- 6 x} ( e ^{6 x} - 1 ) ^{2}}{4} + 1

\frac{e ^{- 6 x} ( e ^{6 x} - 1 ) ^{2}}{4} = \frac{e ^{6 x} - 2 + e ^{- 6 x}}{4}

= \frac{e ^{6 x} + e ^{- 6 x} - 2}{4} + 1

使用分式法则:

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

\frac{e ^{6 x} - 2 + e ^{- 6 x}}{4} = \frac{e ^{6 x}}{4} - \frac{2}{4} + \frac{e ^{- 6 x}}{4}

= \frac{e ^{6 x}}{4} - \frac{2}{4} + \frac{e ^{- 6 x}}{4} + 1

消掉

\frac{2}{4} : \frac{1}{2}

= \frac{e ^{6 x}}{4} - \frac{1}{2} + \frac{e ^{- 6 x}}{4} + 1

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