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Beliebt Rechnen >

integral of (2+tan(x))^2

Lösung

\int (2 + tan (x))^{2} d x

Lösung

3 x - 4 ln ∣ cos (x) ∣ + tan (x) + C

Schritte zur Lösung

\int (2 + tan (x))^{2} d x

Multipliziere aus

(2 + tan (x))^{2} : 4 + 4 tan (x) + tan^{2} (x)

= \int 4 + 4 tan (x) + tan^{2} (x) d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 4 d x + \int 4 tan (x) d x + \int tan^{2} (x) d x

\int 4 d x = 4 x

\int 4 tan (x) d x = - 4 ln ∣ cos (x) ∣

\int tan^{2} (x) d x = - x + tan (x)

= 4 x - 4 ln ∣ cos (x) ∣ - x + tan (x)

Vereinfache

= 3 x - 4 ln ∣ cos (x) ∣ + tan (x)

Füge eine Konstante zur Lösung hinzu

= 3 x - 4 ln ∣ cos (x) ∣ + tan (x) + C

Graph

Beliebte Beispiele

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\int - x^{2} e^{- x} d x