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

Lösung

\int_{0}^{2} \frac{x + 1}{x ^{2} + 1} d x

\frac{1}{2} ln (5) + arctan (2)

Dezimale

1.91186 \dots

Schritte zur Lösung

\int_{0}^{2} \frac{x + 1}{x ^{2} + 1} d x

Multipliziere aus

\frac{x + 1}{x ^{2} + 1} : \frac{x}{x ^{2} + 1} + \frac{1}{x ^{2} + 1}

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} \frac{x}{x ^{2} + 1} d x + \int_{0}^{2} \frac{1}{x ^{2} + 1} d x

\int_{0}^{2} \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln (5)

\int_{0}^{2} \frac{1}{x ^{2} + 1} d x = arctan (2)

= \frac{1}{2} ln (5) + arctan (2)

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