integral from 3 to 4 of ln(x^3-2x^2)

Lösung

\int_{3}^{4} ln (x^{3} - 2 x^{2}) d x

18 ln (2) - 3 - 6 ln (3)

Dezimale

2.88497 \dots

Schritte zur Lösung

\int_{3}^{4} ln (x^{3} - 2 x^{2}) d x

Wende die partielle Integration an

= [x ln (x^{3} - 2 x^{2}) - \int \frac{3 x - 4}{x - 2} d x]_{3}^{4}

\int \frac{3 x - 4}{x - 2} d x = 3 x - 6 + 2 ln ∣ x - 2 ∣

= [x ln (x^{3} - 2 x^{2}) - (3 x - 6 + 2 ln ∣ x - 2 ∣)]_{3}^{4}

Vereinfache

= [x ln (x^{3} - 2 x^{2}) - 3 x + 6 - 2 ln ∣ x - 2 ∣]_{3}^{4}

Berechne die Grenzen:

18 ln (2) - 3 - 6 ln (3)

= 18 ln (2) - 3 - 6 ln (3)

\int_{1}^{6} \frac{7}{x} d x

\int_{0}^{2} (2 x - x) d x

\int_{5}^{6} \frac{6}{x ^{2}} d x

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