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

Lösung

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

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

Dezimale

0.18831 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [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}

Berechne die Grenzen:

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

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

a re a y = - x, x = - 1, x = 2, y = 0

y^{^{''}} + 8 y^{^{'}} + 65 y = 455, y (0) = 0, y^{^{'}} (0) = 0

\int \frac{1}{x ^{2} + 6 x + 18} d x

x \to 1 lim (x - 4)

\int \frac{( arctan ( x ) ) ^{5}}{x ^{2} + 1} d x