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

The integral of (ln(x))/(x^8) is -(ln(x))/(7x^7)-1/(49x^7)+C

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

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

- \frac{ln ( x )}{7 x ^{7}} - \frac{1}{49 x ^{7}} + C

Solution steps

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

Apply Integration By Parts

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

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

\int - \frac{1}{7 x ^{8}} d x = \frac{1}{49 x ^{7}}

= - \frac{ln ( x )}{7 x ^{7}} - \frac{1}{49 x ^{7}}

Add a constant to the solution

= - \frac{ln ( x )}{7 x ^{7}} - \frac{1}{49 x ^{7}} + C

\int_{0}^{1} \frac{33}{4 y - 1} d y

\int_{0}^{\infty} 2 d x

\frac{\partial}{\partial y} (x^{2} cos (x y))

y = x^{3} - 7 x^{2} + 8 x + 1

What is the integral of (ln(x))/(x^8) ?
The integral of (ln(x))/(x^8) is -(ln(x))/(7x^7)-1/(49x^7)+C