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Beliebt Rechnen >

integral of (1-2e^{tan(x)})sec^2(x)

Lösung

\int (1 - 2 e^{t a n (x)}) sec^{2} (x) d x

Lösung

tan (x) - 2 e^{t a n (x)} + C

Schritte zur Lösung

\int (1 - 2 e^{t a n (x)}) sec^{2} (x) d x

Wende U-Substitution an

= \int 1 - 2 e^{u} d u

Wende die Summenregel an:

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

= \int 1 d u - \int 2 e^{u} d u

\int 1 d u = u

\int 2 e^{u} d u = 2 e^{u}

= u - 2 e^{u}

Setze in

u = tan (x)

ein

= tan (x) - 2 e^{t a n (x)}

Füge eine Konstante zur Lösung hinzu

= tan (x) - 2 e^{t a n (x)} + C

Graph

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