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

Lösung

\int (- sec^{2} (x) + e^{2 x + 1}) d x

- tan (x) + \frac{1}{2} e^{2 x + 1} + C

Schritte zur Lösung

\int - sec^{2} (x) + e^{2 x + 1} 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 sec^{2} (x) d x + \int e^{2 x + 1} d x

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

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

= - tan (x) + \frac{1}{2} e^{2 x + 1}

Füge eine Konstante zur Lösung hinzu

= - tan (x) + \frac{1}{2} e^{2 x + 1} + C

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