What is the integral from 2 to 4 of 1/(x^2)ln(x) ?

The integral from 2 to 4 of 1/(x^2)ln(x) is 1/4

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integral from 2 to 4 of 1/(x^2)ln(x)

\int_{2}^{4} \frac{1}{x ^{2}} ln (x) d x

\frac{1}{4}

Decimal Notation

0.25

Solution steps

\int_{2}^{4} \frac{1}{x ^{2}} ln (x) d x

Apply Integration By Parts

: [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{2}^{4}

= [- \frac{ln ( x )}{x} - \int - \frac{1}{x ^{2}} d x]_{2}^{4}

\int - \frac{1}{x ^{2}} d x = \frac{1}{x}

= [- \frac{ln ( x )}{x} - \frac{1}{x}]_{2}^{4}

Since the denominators are equal, combine the fractions:

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= [\frac{- ln ( x ) - 1}{x}]_{2}^{4}

Compute the boundaries:

\frac{1}{4}

= \frac{1}{4}

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What is the integral from 2 to 4 of 1/(x^2)ln(x) ?
The integral from 2 to 4 of 1/(x^2)ln(x) is 1/4