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Beliebt Rechnen >

integral of (x+3)/(x^2+1)

Lösung

\int \frac{x + 3}{x ^{2} + 1} d x

Lösung

\frac{1}{2} ln x^{2} + 1 + 3 arctan (x) + C

Schritte zur Lösung

\int \frac{x + 3}{x ^{2} + 1} d x

Multipliziere aus

\frac{x + 3}{x ^{2} + 1} : \frac{x}{x ^{2} + 1} + \frac{3}{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 \frac{x}{x ^{2} + 1} d x + \int \frac{3}{x ^{2} + 1} d x

\int \frac{x}{x ^{2} + 1} d x = \frac{1}{2} ln x^{2} + 1

\int \frac{3}{x ^{2} + 1} d x = 3 arctan (x)

= \frac{1}{2} ln x^{2} + 1 + 3 arctan (x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 1 + 3 arctan (x) + C

Graph

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