integral of 1/x+x^2-2

Lösung

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

ln ∣ x ∣ + \frac{x ^{3}}{3} - 2 x + C

Schritte zur Lösung

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

\int 2 d x = 2 x

= ln ∣ x ∣ + \frac{x ^{3}}{3} - 2 x

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ + \frac{x ^{3}}{3} - 2 x + C

\int_{- 1}^{0} \frac{4}{1 + ( 2 x + 1 ) ^{2}} d x

t an g e n t x^{3} + 9 x

\int sin (16 x) 3 cos (16 x) d x

\frac{d}{d x} (\frac{2 x}{2 x + 1})

\int_{0}^{N} e^{(- s t)} sin (5 t) d t