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

Lösung

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

\frac{x ^{2}}{2} - 3 x + 5 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} - 3 x + 5}{x} : x - 3 + \frac{5}{x}

= \int x - 3 + \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 d x - \int 3 d x + \int \frac{5}{x} d x

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

\int 3 d x = 3 x

\int \frac{5}{x} d x = 5 ln ∣ x ∣

= \frac{x ^{2}}{2} - 3 x + 5 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - 3 x + 5 ln ∣ x ∣ + C

\int (3 x^{2} - 10) d x

\int \frac{( ln ( y ) ) ^{2}}{y} d y

\int 3 sin^{3} (2 x) cos^{3} (2 x) d x

\int (2 + y^{3})^{2} d y

\int 3 x - 3 x^{5} d x