What is the integral from 1 to 5 of (ln(s))/(s^5) ?

The integral from 1 to 5 of (ln(s))/(s^5) is 39/625-1/2500 ln(5)

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integral from 1 to 5 of (ln(s))/(s^5)

\int_{1}^{5} \frac{ln ( s )}{s ^{5}} d s

\frac{39}{625} - \frac{1}{2500} ln (5)

Decimal Notation

0.06175 \dots

Solution steps

\int_{1}^{5} \frac{ln ( s )}{s ^{5}} d s

Apply Integration By Parts

: [- \frac{ln ( s )}{4 s ^{4}} - \int - \frac{1}{4 s ^{5}} d s]_{1}^{5}

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

\int - \frac{1}{4 s ^{5}} d s = \frac{1}{16 s ^{4}}

= [- \frac{ln ( s )}{4 s ^{4}} - \frac{1}{16 s ^{4}}]_{1}^{5}

Compute the boundaries:

\frac{39}{625} - \frac{1}{2500} ln (5)

= \frac{39}{625} - \frac{1}{2500} ln (5)

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\int_{1}^{4} 4 x - x^{2} d x

What is the integral from 1 to 5 of (ln(s))/(s^5) ?
The integral from 1 to 5 of (ln(s))/(s^5) is 39/625-1/2500 ln(5)