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

Lösung

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

ln (2) + \frac{π}{4}

Dezimale

1.47854 \dots

Schritte zur Lösung

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

Multipliziere aus

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

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

\int_{0}^{1} \frac{1}{x ^{2} + 1} d x = \frac{π}{4}

= ln (2) + \frac{π}{4}

\int_{2}^{5} \frac{k}{x ^{3}} d x

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