What is the integral of (ln(t))/(t^5) ?

The integral of (ln(t))/(t^5) is -(ln(t))/(4t^4)-1/(16t^4)+C

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

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

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

Solution steps

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

Apply Integration By Parts

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

= - \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}}

Add a constant to the solution

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

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What is the integral of (ln(t))/(t^5) ?
The integral of (ln(t))/(t^5) is -(ln(t))/(4t^4)-1/(16t^4)+C