展开 x^{x-1}(ln(x)+(x-1)/x)

解答

展开

x^{x - 1} (ln (x) + \frac{x - 1}{x})

x^{x - 1} ln (x) + x^{x - 1} - x^{x - 2}

求解步骤

x^{x - 1} (ln (x) + \frac{x - 1}{x})

使用分配律:

a (b + c) = ab + a c

a = x^{x - 1}, b = ln (x), c = \frac{x - 1}{x}

= x^{x - 1} ln (x) + x^{x - 1} \frac{x - 1}{x}

= x^{x - 1} ln (x) + \frac{x - 1}{x} x^{x - 1}

\frac{x - 1}{x} x^{x - 1} = x^{x - 1} - x^{x - 2}

= x^{x - 1} ln (x) + x^{x - 1} - x^{x - 2}

e x p an d \frac{2}{( s ( s + 1 ) ( s + 4 ) )}

e x p an d \frac{2 - 2 x ^{2}}{( 1 + x ^{2} ) ^{2}}

s im pl i f y (a + 1 - a - 1)^{2}

e x p an d 2 y d x + x (x^{2} ln (y) - 1) d y

e x p an d sin (5 (t - w))