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

Lösung

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

\frac{x ^{2}}{2} - 6 x + 9 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{( x - 3 ) ^{2}}{x} : x - 6 + \frac{9}{x}

= \int x - 6 + \frac{9}{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 6 d x + \int \frac{9}{x} d x

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

\int 6 d x = 6 x

\int \frac{9}{x} d x = 9 ln ∣ x ∣

= \frac{x ^{2}}{2} - 6 x + 9 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} - 6 x + 9 ln ∣ x ∣ + C

\int x^{\frac{1}{4}} + 5 d x

\int (2 x + 100)^{- 3} d x

\int e y^{2} d y

\int x^{\frac{1}{4}} + 9 d x

\int \frac{x + 1}{1 + x} d x