integral of (ln(14x))/(x^5)

解答

\int \frac{ln ( 14 x )}{x ^{5}} d x

- \frac{ln ( 14 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

求解步骤

\int \frac{ln ( 14 x )}{x ^{5}} d x

使用分布积分法

= - \frac{ln ( 14 x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

\int - \frac{1}{4 x ^{5}} d x = \frac{1}{16 x ^{4}}

= - \frac{ln ( 14 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}

解答补常数

= - \frac{ln ( 14 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

\int \frac{1}{t ^{2} - 2 t + 1} d t

\frac{1}{x ^{2} + y ^{2}} (x d y - y d x) = 0

l a pl a ce t r an s f or m cos (2 (t - \frac{5 π}{4}))

x \to 2 + lim (∣ x - 2 ∣)

\frac{d}{d x} (\frac{1 + csc ( x ^{4} )}{1 - cot ( x ^{4} )})