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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\int (3 x + 4)^{3} d x

n = 0 \sum \infty 16 + 24 + 36 + 54

\frac{\partial}{\partial x} (e^{5 x y} 5 y)

\frac{1}{x ^{2} - 1}

\frac{d}{d x} (1 + \frac{1}{x})

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