What is the integral of 1/(x^3)ln(x) ?

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

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integral of 1/(x^3)ln(x)

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

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

Solution steps

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

Simplify

\frac{1}{x ^{3}} ln (x) : \frac{ln ( x )}{x ^{3}}

= \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{\partial}{\partial y} (x^{2})

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

\int_{0}^{1} 2 x 1 + 4 x^{2} d x

\frac{d}{d t} (- cos (t))

\int_{- 2}^{3} (x^{3} - 4 x) d x

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