What is the integral of (ln(6x))/(x^4) ?

The integral of (ln(6x))/(x^4) is -(ln(6x))/(3x^3)-1/(9x^3)+C

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integral of (ln(6x))/(x^4)

\int \frac{ln ( 6 x )}{x ^{4}} d x

- \frac{ln ( 6 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

Solution steps

\int \frac{ln ( 6 x )}{x ^{4}} d x

Apply Integration By Parts

: - \frac{ln ( 6 x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

= - \frac{ln ( 6 x )}{3 x ^{3}} - \int - \frac{1}{3 x ^{4}} d x

\int - \frac{1}{3 x ^{4}} d x = \frac{1}{9 x ^{3}}

= - \frac{ln ( 6 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}

Add a constant to the solution

= - \frac{ln ( 6 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

\int_{1}^{2} x d x

\frac{\partial}{\partial z} (arctan (\frac{y}{x}))

\int \frac{1}{x ^{2} \cdot 9 - x ^{2}} d x

\int \frac{x ^{2} - x + 10}{( x + 2 ) ( x ^{2} + 4 )} d x

\frac{\partial}{\partial x} (2 x^{3} + x^{2} y^{3} - 3 y^{2})

What is the integral of (ln(6x))/(x^4) ?
The integral of (ln(6x))/(x^4) is -(ln(6x))/(3x^3)-1/(9x^3)+C