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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

fläche x^2+10,9x,0

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integral of ((9-y^2)^2)/2-y(9-y^2)

\int \frac{( 9 - y ^{2} ) ^{2}}{2} - y (9 - y^{2}) d y

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\int y + 4 d y

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\frac{d}{d x} (\frac{2 x}{x ^{4} + 1})

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\int_{1}^{4} - 10 t ln (t) d t