integral of 5x^2-4/x+a

Lösung

\int 5 x^{2} - \frac{4}{x} + a d x

\frac{5 x ^{3}}{3} - 4 ln ∣ x ∣ + a x + C

Schritte zur Lösung

\int 5 x^{2} - \frac{4}{x} + a 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 5 x^{2} d x - \int \frac{4}{x} d x + \int a d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int \frac{4}{x} d x = 4 ln ∣ x ∣

\int a d x = a x

= \frac{5 x ^{3}}{3} - 4 ln ∣ x ∣ + a x

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{3}}{3} - 4 ln ∣ x ∣ + a x + C

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

\int (5 z^{2} - 3)^{3} z d z

\frac{\partial}{\partial x} (e^{7 y} sin (- 7 x))

\frac{d}{d x} (\frac{1}{arctan ( x )})

\int (2 x - 40) ln (x - 20) d x