What is the integral from 1 to 3 of (ln(x))/(x^9) ?

The integral from 1 to 3 of (ln(x))/(x^9) is 205/13122-1/52488 ln(3)

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integral from 1 to 3 of (ln(x))/(x^9)

\int_{1}^{3} \frac{ln ( x )}{x ^{9}} d x

\frac{205}{13122} - \frac{1}{52488} ln (3)

Decimal

0.01560 \dots

Solution steps

\int_{1}^{3} \frac{ln ( x )}{x ^{9}} d x

Apply Integration By Parts

= [- \frac{ln ( x )}{8 x ^{8}} - \int - \frac{1}{8 x ^{9}} d x]_{1}^{3}

\int - \frac{1}{8 x ^{9}} d x = \frac{1}{64 x ^{8}}

= [- \frac{ln ( x )}{8 x ^{8}} - \frac{1}{64 x ^{8}}]_{1}^{3}

Compute the boundaries:

\frac{205}{13122} - \frac{1}{52488} ln (3)

= \frac{205}{13122} - \frac{1}{52488} ln (3)

What is the integral from 1 to 3 of (ln(x))/(x^9) ?
The integral from 1 to 3 of (ln(x))/(x^9) is 205/13122-1/52488 ln(3)