integral of ([ln(x)]^3)/x

解答

\int \frac{[ ln ( x ) ] ^{3}}{x} d x

\frac{ln ^{4} ( x )}{4} + C

求解步骤

\int \frac{[ ln ( x ) ] ^{3}}{x} d x

化简

= \int \frac{ln ^{3} ( x )}{x} d x

使用换元积分法

= \int u^{3} d u

使用幂法则

= \frac{u ^{4}}{4}

u = ln (x)

代回

= \frac{ln ^{4} ( x )}{4}

解答补常数

= \frac{ln ^{4} ( x )}{4} + C

\int (x^{8} - 25)^{9} x^{7} d x

\frac{d y}{d x} = y e^{- x}

\int x^{\frac{7}{2}} d x

\frac{d}{d x} ((3 + cos^{3} (3 x))^{- \frac{1}{3}})

x \to 3 lim (2 x^{2} + 6)