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

The integral of (ln(x))/(x^6) is -(ln(x))/(5x^5)-1/(25x^5)+C

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

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

- \frac{ln ( x )}{5 x ^{5}} - \frac{1}{25 x ^{5}} + C

Solution steps

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

Apply Integration By Parts

: - \frac{ln ( x )}{5 x ^{5}} - \int - \frac{1}{5 x ^{6}} d x

= - \frac{ln ( x )}{5 x ^{5}} - \int - \frac{1}{5 x ^{6}} d x

\int - \frac{1}{5 x ^{6}} d x = \frac{1}{25 x ^{5}}

= - \frac{ln ( x )}{5 x ^{5}} - \frac{1}{25 x ^{5}}

Add a constant to the solution

= - \frac{ln ( x )}{5 x ^{5}} - \frac{1}{25 x ^{5}} + C

y = sin (x), at x = \frac{π}{4}

\int \frac{1}{( x + 1 ) ^{2} + 4} d x

\int x^{2} x^{3} + 33 d x

\frac{d y}{d x} + y^{5} x + 2 y = 0

\int \frac{1}{x ^{5} x ^{2} - 1} d x

What is the integral of (ln(x))/(x^6) ?
The integral of (ln(x))/(x^6) is -(ln(x))/(5x^5)-1/(25x^5)+C