What is the integral from 1 to 3 of pi(ln(x))^2 ?

The integral from 1 to 3 of pi(ln(x))^2 is pi(3ln^2(3)-6ln(3)+4)

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integral from 1 to 3 of pi(ln(x))^2

\int_{1}^{3} π (ln (x))^{2} d x

π (3 ln^{2} (3) - 6 ln (3) + 4)

Decimal Notation

3.23324 \dots

Solution steps

\int_{1}^{3} π (ln (x))^{2} d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= π \cdot \int_{1}^{3} (ln (x))^{2} d x

Apply Integration By Parts

: [x ln^{2} (x) - \int 2 ln (x) d x]_{1}^{3}

= π [x ln^{2} (x) - \int 2 ln (x) d x]_{1}^{3}

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

= π [x ln^{2} (x) - 2 (x ln (x) - x)]_{1}^{3}

Compute the boundaries:

3 ln^{2} (3) - 6 ln (3) + 4

= π (3 ln^{2} (3) - 6 ln (3) + 4)

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

\int_{0}^{1} 4 - x d x

\int_{- 2}^{- 1} - x^{2} - 2 x + 3 d x

\int_{3}^{5} x^{\frac{3}{2}} d x

\int_{0}^{2} 2 t e^{- t^{2}} d t

What is the integral from 1 to 3 of pi(ln(x))^2 ?
The integral from 1 to 3 of pi(ln(x))^2 is pi(3ln^2(3)-6ln(3)+4)