integral from 0 to 0.37 of ln(1+x^2)

Lösung

\int_{0}^{0.37} ln (1 + x^{2}) d x

0.01623 \dots

Schritte zur Lösung

\int_{0}^{0.37} ln (1 + x^{2}) d x

Wende die partielle Integration an

= [x ln (1 + x^{2}) - \int \frac{2 x ^{2}}{1 + x ^{2}} d x]_{0}^{0.37}

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

= [x ln (1 + x^{2}) - 2 (- arctan (x) + x)]_{0}^{0.37}

Berechne die Grenzen:

0.01623 \dots

= 0.01623 \dots