integral of ln(1/x)

解答

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

- x ln (x) + x + C

求解步骤

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

使用分布积分法

= - x ln (x) - \int - 1 d x

\int - 1 d x = - x

= - x ln (x) - (- x)

化简

= - x ln (x) + x

解答补常数

= - x ln (x) + x + C

\frac{d y}{d t} = (a \cdot 2) - \frac{y}{20} 2, y (0) = 0

\frac{d y}{d x} = x (4 x + 5)^{\frac{1}{3}}

f (x) = 2 x - x^{2}

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

\int (\frac{2}{3} sec (x) tan (x)) d x