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

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

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

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

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

Decimal

0.18831 \dots

Solution steps

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

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

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

= 2 ln^{2} (2) - 4 ln (2) + 2

\int_{1}^{2} (x^{2} - 1) d x

\int_{1}^{x} e^{t^{2}} d t

\int_{0}^{2} x^{2} f (x^{3} + 1) d x

\int_{- π}^{π} 1 d x

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

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