What is the integral from 1 to 2 of (ln(x))/(x^6) ?

The integral from 1 to 2 of (ln(x))/(x^6) is 31/800-1/160 ln(2)

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integral from 1 to 2 of (ln(x))/(x^6)

\int_{1}^{2} \frac{ln ( x )}{x ^{6}} d x

\frac{31}{800} - \frac{1}{160} ln (2)

Decimal Notation

0.03441 \dots

Solution steps

\int_{1}^{2} \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}^{2}

= [- \frac{ln ( x )}{5 x ^{5}} - \int - \frac{1}{5 x ^{6}} d x]_{1}^{2}

\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}^{2}

Compute the boundaries:

\frac{31}{800} - \frac{1}{160} ln (2)

= \frac{31}{800} - \frac{1}{160} ln (2)

\int_{0}^{\frac{π}{2}} (- 3 x^{2} + x - 2) d x

\int_{0}^{1} \frac{x ^{4}}{x ^{5} + 1} d x

\int_{- 2}^{0} (4 x^{3} + x^{2} - 2 x) d x

\int_{0}^{1} (2 t + 5) (e^{- t}) d t

\int_{0}^{\infty} π e^{- 2 x} d x

What is the integral from 1 to 2 of (ln(x))/(x^6) ?
The integral from 1 to 2 of (ln(x))/(x^6) is 31/800-1/160 ln(2)