What is the integral of (ln(8x))/(x^7) ?

The integral of (ln(8x))/(x^7) is -(ln(8x))/(6x^6)-1/(36x^6)+C

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integral of (ln(8x))/(x^7)

\int \frac{ln ( 8 x )}{x ^{7}} d x

- \frac{ln ( 8 x )}{6 x ^{6}} - \frac{1}{36 x ^{6}} + C

Solution steps

\int \frac{ln ( 8 x )}{x ^{7}} d x

Apply Integration By Parts

= - \frac{ln ( 8 x )}{6 x ^{6}} - \int - \frac{1}{6 x ^{7}} d x

\int - \frac{1}{6 x ^{7}} d x = \frac{1}{36 x ^{6}}

= - \frac{ln ( 8 x )}{6 x ^{6}} - \frac{1}{36 x ^{6}}

Add a constant to the solution

= - \frac{ln ( 8 x )}{6 x ^{6}} - \frac{1}{36 x ^{6}} + C

\int x^{2} (2 x + 5)^{2} d x

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

\int x^{2} (x^{2} + 6)^{- \frac{1}{2}} d x

\int \frac{48}{1 + 36 x ^{2}} d x

\int 8 x (4 x^{2} + 9)^{4} d x

What is the integral of (ln(8x))/(x^7) ?
The integral of (ln(8x))/(x^7) is -(ln(8x))/(6x^6)-1/(36x^6)+C