What is the integral from 2 to 5 of (ln(x))^2 ?

The integral from 2 to 5 of (ln(x))^2 is -2ln^2(2)+4ln(2)+5ln^2(5)+6-10ln(5)

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integral from 2 to 5 of (ln(x))^2

\int_{2}^{5} (ln (x))^{2} d x

- 2 ln^{2} (2) + 4 ln (2) + 5 ln^{2} (5) + 6 - 10 ln (5)

Decimal Notation

4.66875 \dots

Solution steps

\int_{2}^{5} (ln (x))^{2} d x

Apply Integration By Parts

: [x ln^{2} (x) - \int 2 ln (x) d x]_{2}^{5}

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

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

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{2}^{5}

Compute the boundaries:

- 2 ln^{2} (2) + 4 ln (2) + 5 ln^{2} (5) + 6 - 10 ln (5)

= - 2 ln^{2} (2) + 4 ln (2) + 5 ln^{2} (5) + 6 - 10 ln (5)

\int_{0}^{\infty} A e^{- λ t} d t

\int_{0}^{t} e^{- 3 u} d u

\int_{a}^{b} [3 f (t) - 2 g (t)] d t

\int_{1}^{2} x^{\frac{3}{2}} d x

\int_{1}^{4} \frac{1}{5 - x} d x

What is the integral from 2 to 5 of (ln(x))^2 ?
The integral from 2 to 5 of (ln(x))^2 is -2ln^2(2)+4ln(2)+5ln^2(5)+6-10ln(5)