What is the integral of (ln(x^3))/(x^5) ?

The integral of (ln(x^3))/(x^5) is 3(-(ln(x))/(4x^4)-1/(16x^4))+C

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integral of (ln(x^3))/(x^5)

\int \frac{ln ( x ^{3} )}{x ^{5}} d x

3 (- \frac{ln ( x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}) + C

Solution steps

\int \frac{ln ( x ^{3} )}{x ^{5}} d x

Simplify

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

= \int \frac{3 ln ( x )}{x ^{5}} 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 ^{5}} d x

Apply Integration By Parts

: - \frac{ln ( x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

= 3 (- \frac{ln ( x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x)

\int - \frac{1}{4 x ^{5}} d x = \frac{1}{16 x ^{4}}

= 3 (- \frac{ln ( x )}{4 x ^{4}} - \frac{1}{16 x ^{4}})

Add a constant to the solution

= 3 (- \frac{ln ( x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}) + C

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What is the integral of (ln(x^3))/(x^5) ?
The integral of (ln(x^3))/(x^5) is 3(-(ln(x))/(4x^4)-1/(16x^4))+C