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Beliebt Rechnen >

integral of (e^{arctan(x)}-2x)/(1+x^2)

Lösung

\int \frac{e ^{a r c t a n (x)} - 2 x}{1 + x ^{2}} d x

Lösung

e^{a r c t a n (x)} - ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{e ^{a r c t a n (x)} - 2 x}{1 + x ^{2}} d x

Multipliziere aus

\frac{e ^{a r c t a n (x)} - 2 x}{1 + x ^{2}} : \frac{e ^{a r c t a n (x)}}{1 + x ^{2}} - \frac{2 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{e ^{a r c t a n (x)}}{1 + x ^{2}} d x - \int \frac{2 x}{1 + x ^{2}} d x

\int \frac{e ^{a r c t a n (x)}}{1 + x ^{2}} d x = e^{a r c t a n (x)}

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

= e^{a r c t a n (x)} - ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= e^{a r c t a n (x)} - ln 1 + x^{2} + C

Graph

Beliebte Beispiele

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\int (x + 4) e^{- 2 x} d x

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