integral from 1 to 2 of ln((4x)^2)

Lösung

\int_{1}^{2} ln ((4 x)^{2}) d x

8 ln (2) - 2

Dezimale

3.54517 \dots

Schritte zur Lösung

\int_{1}^{2} ln ((4 x)^{2}) d x

Wende die partielle Integration an

= [x ln (16 x^{2}) - \int 2 d x]_{1}^{2}

\int 2 d x = 2 x

= [x ln (16 x^{2}) - 2 x]_{1}^{2}

Vereinfache

ln (16 x^{2}) : 2 (ln (x) + 2 ln (2))

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

Berechne die Grenzen:

8 ln (2) - 2

= 8 ln (2) - 2

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