integral of (x-2/x-4e^{4x})

Lösung

\int (x - \frac{2}{x} - 4 e^{4 x}) d x

\frac{x ^{2}}{2} - 2 ln ∣ x ∣ - e^{4 x} + C

Schritte zur Lösung

\int x - \frac{2}{x} - 4 e^{4 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 x d x - \int \frac{2}{x} d x - \int 4 e^{4 x} d x

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

\int 4 e^{4 x} d x = e^{4 x}

= \frac{x ^{2}}{2} - 2 ln ∣ x ∣ - e^{4 x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - 2 ln ∣ x ∣ - e^{4 x} + C

\int \frac{6 x - 7}{3 x ^{2} - 7 x + 15} d x

\int y e^{3 t^{2}} d t

\int \frac{25 - x ^{2}}{15 x ^{2}} d x

\int 36 - x^{2} (- 2 x) d x

\int arcsec (m x) d x