integral of (2e^x+6/x+ln(2))

Lösung

\int (2 e^{x} + \frac{6}{x} + ln (2)) d x

2 e^{x} + 6 ln ∣ x ∣ + ln (2) x + C

Schritte zur Lösung

\int 2 e^{x} + \frac{6}{x} + ln (2) 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 2 e^{x} d x + \int \frac{6}{x} d x + \int ln (2) d x

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

\int \frac{6}{x} d x = 6 ln ∣ x ∣

\int ln (2) d x = ln (2) x

= 2 e^{x} + 6 ln ∣ x ∣ + ln (2) x

Füge eine Konstante zur Lösung hinzu

= 2 e^{x} + 6 ln ∣ x ∣ + ln (2) x + C

\int e^{- x} cos (\frac{x}{2}) d x

\int e^{\frac{2}{5} x} d x

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

\int \frac{1}{x ^{2} + 4 x + 29} d x

\int 11 sin^{3} (x) cos^{2} (x) d x