integral of (3+6x)/(1+x^2)

Lösung

\int \frac{3 + 6 x}{1 + x ^{2}} d x

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

Schritte zur Lösung

\int \frac{3 + 6 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{3 + 6 x}{1 + x ^{2}} : \frac{3}{1 + x ^{2}} + \frac{6 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{6 x}{1 + x ^{2}} d x

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

\int \frac{6 x}{1 + x ^{2}} d x = 3 ln 1 + x^{2}

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

Füge eine Konstante zur Lösung hinzu

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

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