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

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

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

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

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

Decimal Notation

0.06175 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

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

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

f (x) = 4 x^{3} - 11 x^{2} - 14 x + 19

x \to 0 lim ((\frac{1 + tan ( x )}{1 + sin ( x )})^{\frac{1}{s i n ( x )}})

\int_{6}^{8} \frac{82}{( x - 6 ) ^{3}} d x

\frac{d}{d x} ((2 x - x^{2})^{3})

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

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