What is the integral of (ln(x^3))/(x^2) ?

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

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integral of (ln(x^3))/(x^2)

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

3 (- \frac{ln ( x )}{x} - \frac{1}{x}) + C

Solution steps

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

Simplify

ln (x^{3}) : 3 ln (x)

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

Take the constant out:

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

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

Apply Integration By Parts

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

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

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

= 3 (- \frac{ln ( x )}{x} - \frac{1}{x})

Add a constant to the solution

= 3 (- \frac{ln ( x )}{x} - \frac{1}{x}) + C

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