integral of (1/x+4sin(2x)+e^x)

Lösung

\int (\frac{1}{x} + 4 sin (2 x) + e^{x}) d x

ln ∣ x ∣ - 2 cos (2 x) + e^{x} + C

Schritte zur Lösung

\int \frac{1}{x} + 4 sin (2 x) + e^{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 \frac{1}{x} d x + \int 4 sin (2 x) d x + \int e^{x} d x

\int \frac{1}{x} d x = ln ∣ x ∣

\int 4 sin (2 x) d x = - 2 cos (2 x)

\int e^{x} d x = e^{x}

= ln ∣ x ∣ - 2 cos (2 x) + e^{x}

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - 2 cos (2 x) + e^{x} + C

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