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

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

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integral of (ln(y))/(y^3)

\int \frac{ln ( y )}{y ^{3}} d y

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

Solution steps

\int \frac{ln ( y )}{y ^{3}} d y

Apply Integration By Parts

: - \frac{ln ( y )}{2 y ^{2}} - \int - \frac{1}{2 y ^{3}} d y

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

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

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

Add a constant to the solution

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

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