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

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

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

integral

\frac{ln ( 4 x )}{x ^{4}}

- \frac{ln ( 4 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

Solution steps

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

Apply Integration By Parts

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

= - \frac{ln ( 4 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 ( 4 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}}

Add a constant to the solution

= - \frac{ln ( 4 x )}{3 x ^{3}} - \frac{1}{9 x ^{3}} + C

\frac{1}{( 5 + x ^{2} )}

e^{2} x - 1

(\frac{1}{x - 1})^{\frac{- 1}{2}}

\frac{x}{( x ^{2} - 1 ) ^{\frac{1}{2}}}

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

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