What is the integral from 1 to 4 of (ln(x))/(x^6) ?

The integral from 1 to 4 of (ln(x))/(x^6) is 1023/25600-1/2560 ln(2)

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integral from 1 to 4 of (ln(x))/(x^6)

\int_{1}^{4} \frac{ln ( x )}{x ^{6}} d x

\frac{1023}{25600} - \frac{1}{2560} ln (2)

Decimal Notation

0.03969 \dots

Solution steps

\int_{1}^{4} \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]_{1}^{4}

= [- \frac{ln ( x )}{5 x ^{5}} - \int - \frac{1}{5 x ^{6}} d x]_{1}^{4}

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

= [- \frac{ln ( x )}{5 x ^{5}} - \frac{1}{25 x ^{5}}]_{1}^{4}

Compute the boundaries:

\frac{1023}{25600} - \frac{1}{2560} ln (2)

= \frac{1023}{25600} - \frac{1}{2560} ln (2)

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What is the integral from 1 to 4 of (ln(x))/(x^6) ?
The integral from 1 to 4 of (ln(x))/(x^6) is 1023/25600-1/2560 ln(2)