What is the integral of (ln(14x))/(x^5) ?

The integral of (ln(14x))/(x^5) is -(ln(14x))/(4x^4)-1/(16x^4)+C

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integral of (ln(14x))/(x^5)

\int \frac{ln ( 14 x )}{x ^{5}} d x

- \frac{ln ( 14 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

Solution steps

\int \frac{ln ( 14 x )}{x ^{5}} d x

Apply Integration By Parts

: - \frac{ln ( 14 x )}{4 x ^{4}} - \int - \frac{1}{4 x ^{5}} d x

= - \frac{ln ( 14 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}}

= - \frac{ln ( 14 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}}

Add a constant to the solution

= - \frac{ln ( 14 x )}{4 x ^{4}} - \frac{1}{16 x ^{4}} + C

\int \frac{1}{t ^{2} - 2 t + 1} d t

\frac{1}{x ^{2} + y ^{2}} (x d y - y d x) = 0

cos (2 (t - \frac{5 π}{4}))

x \to 2 + lim (∣ x - 2 ∣)

\int 5 e^{2 x} + \frac{1}{x} d x

What is the integral of (ln(14x))/(x^5) ?
The integral of (ln(14x))/(x^5) is -(ln(14x))/(4x^4)-1/(16x^4)+C