integral of (7ln(x))/(x^3)

解答

\int \frac{7 ln ( x )}{x ^{3}} d x

7 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) + C

求解步骤

\int \frac{7 ln ( x )}{x ^{3}} d x

提出常数:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 7 \cdot \int \frac{ln ( x )}{x ^{3}} d x

使用分布积分法

= 7 (- \frac{ln ( x )}{2 x ^{2}} - \int - \frac{1}{2 x ^{3}} d x)

\int - \frac{1}{2 x ^{3}} d x = \frac{1}{4 x ^{2}}

= 7 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}})

解答补常数

= 7 (- \frac{ln ( x )}{2 x ^{2}} - \frac{1}{4 x ^{2}}) + C

ma c l a u r in ln (2 + x)

\frac{d}{d x} (5 arctan (x + 1 + x^{2}))

\frac{d y}{d x} = 0.0015 y (1200 - y)

\int \frac{1}{7 - 8 x} d x

\frac{\partial}{\partial x} (7 x^{2} + e^{2 y})