What is the integral from 1 to 2 of (ln(x))/(x^{10)} ?

The integral from 1 to 2 of (ln(x))/(x^{10)} is 511/41472-1/4608 ln(2)

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integral from 1 to 2 of (ln(x))/(x^{10)}

\int_{1}^{2} \frac{ln ( x )}{x ^{10}} d x

\frac{511}{41472} - \frac{1}{4608} ln (2)

Decimal

0.01217 \dots

Solution steps

\int_{1}^{2} \frac{ln ( x )}{x ^{10}} d x

Apply Integration By Parts

: [- \frac{ln ( x )}{9 x ^{9}} - \int - \frac{1}{9 x ^{10}} d x]_{1}^{2}

= [- \frac{ln ( x )}{9 x ^{9}} - \int - \frac{1}{9 x ^{10}} d x]_{1}^{2}

\int - \frac{1}{9 x ^{10}} d x = \frac{1}{81 x ^{9}}

= [- \frac{ln ( x )}{9 x ^{9}} - \frac{1}{81 x ^{9}}]_{1}^{2}

Compute the boundaries:

\frac{511}{41472} - \frac{1}{4608} ln (2)

= \frac{511}{41472} - \frac{1}{4608} ln (2)

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What is the integral from 1 to 2 of (ln(x))/(x^{10)} ?
The integral from 1 to 2 of (ln(x))/(x^{10)} is 511/41472-1/4608 ln(2)