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Beliebt Rechnen >

integral of (x+1)/(x^2+16)

Lösung

\int \frac{x + 1}{x ^{2} + 16} d x

Lösung

\frac{1}{2} ln x^{2} + 16 + \frac{1}{4} arctan (\frac{x}{4}) + C

Schritte zur Lösung

\int \frac{x + 1}{x ^{2} + 16} d x

Multipliziere aus

\frac{x + 1}{x ^{2} + 16} : \frac{x}{x ^{2} + 16} + \frac{1}{x ^{2} + 16}

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} + 16} d x + \int \frac{1}{x ^{2} + 16} d x

\int \frac{x}{x ^{2} + 16} d x = \frac{1}{2} ln x^{2} + 16

\int \frac{1}{x ^{2} + 16} d x = \frac{1}{4} arctan (\frac{x}{4})

= \frac{1}{2} ln x^{2} + 16 + \frac{1}{4} arctan (\frac{x}{4})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} ln x^{2} + 16 + \frac{1}{4} arctan (\frac{x}{4}) + C

Graph

Beliebte Beispiele

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\frac{d}{d x} (- 2 x e^{- 2 x})

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

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

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

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