What is the integral of (ln(t))/(t^6) ?

The integral of (ln(t))/(t^6) is -(ln(t))/(5t^5)-1/(25t^5)+C

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integral of (ln(t))/(t^6)

\int \frac{ln ( t )}{t ^{6}} d t

- \frac{ln ( t )}{5 t ^{5}} - \frac{1}{25 t ^{5}} + C

Solution steps

\int \frac{ln ( t )}{t ^{6}} d t

Apply Integration By Parts

: - \frac{ln ( t )}{5 t ^{5}} - \int - \frac{1}{5 t ^{6}} d t

= - \frac{ln ( t )}{5 t ^{5}} - \int - \frac{1}{5 t ^{6}} d t

\int - \frac{1}{5 t ^{6}} d t = \frac{1}{25 t ^{5}}

= - \frac{ln ( t )}{5 t ^{5}} - \frac{1}{25 t ^{5}}

Add a constant to the solution

= - \frac{ln ( t )}{5 t ^{5}} - \frac{1}{25 t ^{5}} + C

\int_{2}^{4} (x - 2) d x

\int (\frac{3 + 5 x - 6 x ^{2} - 7 x ^{3}}{2 x ^{2}}) d x

f (x) = x^{2} - 5 x + 5, at x = 4

2 x^{3} + 3 x^{2} - 12 x + 4

cos (6 x)

What is the integral of (ln(t))/(t^6) ?
The integral of (ln(t))/(t^6) is -(ln(t))/(5t^5)-1/(25t^5)+C