integral of x^{sqrt(2)}-3/(sqrt(x))+5/x

Lösung

\int x^{2} - \frac{3}{x} + \frac{5}{x} d x

(2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣ + C

Schritte zur Lösung

\int x^{2} - \frac{3}{x} + \frac{5}{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^{2} d x - \int \frac{3}{x} d x + \int \frac{5}{x} d x

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

\int \frac{3}{x} d x = 6 x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= (2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= (2 - 1) x^{2 + 1} - 6 x + 5 ln ∣ x ∣ + C

\int e^{8 x + 9} d x

\int 3 x^{2} (e^{x^{3}} - 1) d x

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

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

\int 6 x^{2} - 7 d x