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

Lösung

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

4 arctan (3) + 6 ln (40) - 12

Dezimale

15.12945 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [x ln (4 x^{2} + 4) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{- 3}^{3}

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

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

Berechne die Grenzen:

4 arctan (3) + 6 ln (40) - 12

= 4 arctan (3) + 6 ln (40) - 12

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