What is the integral from 3 to 4 of (ln(x))^2 ?

The integral from 3 to 4 of (ln(x))^2 is 16ln^2(2)-16ln(2)+2+6ln(3)-3ln^2(3)

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integral from 3 to 4 of (ln(x))^2

\int_{3}^{4} (ln (x))^{2} d x

16 ln^{2} (2) - 16 ln (2) + 2 + 6 ln (3) - 3 ln^{2} (3)

Decimal

1.56772 \dots

Solution steps

\int_{3}^{4} (ln (x))^{2} d x

Apply Integration By Parts

: [x ln^{2} (x) - \int 2 ln (x) d x]_{3}^{4}

= [x ln^{2} (x) - \int 2 ln (x) d x]_{3}^{4}

\int 2 ln (x) d x = 2 (x ln (x) - x)

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{3}^{4}

Compute the boundaries:

16 ln^{2} (2) - 16 ln (2) + 2 + 6 ln (3) - 3 ln^{2} (3)

= 16 ln^{2} (2) - 16 ln (2) + 2 + 6 ln (3) - 3 ln^{2} (3)

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What is the integral from 3 to 4 of (ln(x))^2 ?
The integral from 3 to 4 of (ln(x))^2 is 16ln^2(2)-16ln(2)+2+6ln(3)-3ln^2(3)