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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d v}{d t} = - k v

\frac{d y}{d x} - \frac{7 y}{x} = \frac{y ^{3}}{x ^{9}}

\frac{d}{d x} (\frac{3 x ^{2}}{2 x + 1})

\frac{d y}{d x} = \frac{( x - 2 )}{( y - 2 )}

(1 + cos (t)) \frac{d y}{d t} = (1 - e^{- y}) sin (t)

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