integral from 0 to 3 of ln(x^2+1)

Lösung

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

3 ln (10) - 2 (- arctan (3) + 3)

Dezimale

3.40584 \dots

Schritte zur Lösung

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

Wende die partielle Integration an

= [x ln (x^{2} + 1) - \int \frac{2 x ^{2}}{x ^{2} + 1} d x]_{0}^{3}

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

= [x ln (x^{2} + 1) - 2 (- arctan (x) + x)]_{0}^{3}

Berechne die Grenzen:

3 ln (10) - 2 (- arctan (3) + 3)

= 3 ln (10) - 2 (- arctan (3) + 3)