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

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

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

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

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

Solution steps

\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

= - \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}}

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

Add a constant to the solution

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

\int_{0}^{4} x^{2} (4 - x)^{3} d x

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

\frac{d}{d x} (10 (20 x - x^{\frac{3}{2}}))

x \to 1 lim (\frac{x}{x ^{2} + 7})

y^{^{''}} + 6 y^{^{'}} + 10 y = 0

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