integral of (ln(t))/(t^5)

解答

\int \frac{ln ( t )}{t ^{5}} d t

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

求解步骤

\int \frac{ln ( t )}{t ^{5}} d t

使用分布积分法

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

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

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

解答补常数

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

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