What is the integral of (ln(t))/(7t^3) ?

The integral of (ln(t))/(7t^3) is 1/7 (-(ln(t))/(2t^2)-1/(4t^2))+C

integral of (ln(t))/(7t^3)

\int \frac{ln ( t )}{7 t ^{3}} d t

\frac{1}{7} (- \frac{ln ( t )}{2 t ^{2}} - \frac{1}{4 t ^{2}}) + C

Solution steps

\int \frac{ln ( t )}{7 t ^{3}} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{7} \cdot \int \frac{ln ( t )}{t ^{3}} d t

Apply Integration By Parts

= \frac{1}{7} (- \frac{ln ( t )}{2 t ^{2}} - \int - \frac{1}{2 t ^{3}} d t)

\int - \frac{1}{2 t ^{3}} d t = \frac{1}{4 t ^{2}}

= \frac{1}{7} (- \frac{ln ( t )}{2 t ^{2}} - \frac{1}{4 t ^{2}})

Add a constant to the solution

= \frac{1}{7} (- \frac{ln ( t )}{2 t ^{2}} - \frac{1}{4 t ^{2}}) + C

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What is the integral of (ln(t))/(7t^3) ?
The integral of (ln(t))/(7t^3) is 1/7 (-(ln(t))/(2t^2)-1/(4t^2))+C