integral of 1/(x(ln(x))^{10)}

解答

\int \frac{1}{x ( ln ( x ) ) ^{10}} d x

- \frac{1}{9 ln ^{9} ( x )} + C

求解步骤

\int \frac{1}{x ( ln ( x ) ) ^{10}} d x

化简

= \int \frac{1}{x ln ^{10} ( x )} d x

使用换元积分法

= \int \frac{1}{u ^{10}} d u

使用幂法则

= - \frac{1}{9 u ^{9}}

u = ln (x)

代回

= - \frac{1}{9 ln ^{9} ( x )}

解答补常数

= - \frac{1}{9 ln ^{9} ( x )} + C

\frac{d}{d x} (\frac{tan ^{3} ( x )}{2 x + 1})

\int sin (4 - x) d x

x \to 0 lim (ln ∣ sin (x) ∣)

\frac{d}{d x} (\frac{4 x ^{3}}{3} - x + 2 e^{x})

18 y^{^{''}} - 9 y^{^{'}} - 5 y = 0