integral of sec(x)tan(x)+3/x-e^x

Lösung

\int sec (x) tan (x) + \frac{3}{x} - e^{x} d x

sec (x) + 3 ln ∣ x ∣ - e^{x} + C

Schritte zur Lösung

\int sec (x) tan (x) + \frac{3}{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 sec (x) tan (x) d x + \int \frac{3}{x} d x - \int e^{x} d x

\int sec (x) tan (x) d x = sec (x)

\int \frac{3}{x} d x = 3 ln ∣ x ∣

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

= sec (x) + 3 ln ∣ x ∣ - e^{x}

Füge eine Konstante zur Lösung hinzu

= sec (x) + 3 ln ∣ x ∣ - e^{x} + C

\int (6 x^{2} + 3 x + \frac{1}{x ^{3}}) d x

\int 8 x^{6} d x

\int \frac{4}{3 - 2 x} d x

\int \frac{1}{2 x + 1 - x} d x

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