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

Lösung

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

x ln (x^{2} + 1) - 2 (x - arctan (x))

Schritte zur Lösung

\int_{0}^{x} 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}^{x}

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

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

Berechne die Grenzen:

x ln (x^{2} + 1) - 2 (x - arctan (x))

= x ln (x^{2} + 1) - 2 (x - arctan (x))

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

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