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

Lösung

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

\frac{1}{2} (x + 3)^{2} - 6 x - 18 + 7 ln ∣ x + 3 ∣ + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{x ^{2}}{x + 3} d x = \frac{( x + 3 ) ^{2}}{2} - 6 (x + 3) + 9 ln ∣ x + 3 ∣

\int \frac{2}{x + 3} d x = 2 ln ∣ x + 3 ∣

= \frac{( x + 3 ) ^{2}}{2} - 6 (x + 3) + 9 ln ∣ x + 3 ∣ - 2 ln ∣ x + 3 ∣

Vereinfache

\frac{( x + 3 ) ^{2}}{2} - 6 (x + 3) + 9 ln ∣ x + 3 ∣ - 2 ln ∣ x + 3 ∣ : \frac{1}{2} (x + 3)^{2} - 6 x - 18 + 7 ln ∣ x + 3 ∣

= \frac{1}{2} (x + 3)^{2} - 6 x - 18 + 7 ln ∣ x + 3 ∣

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} (x + 3)^{2} - 6 x - 18 + 7 ln ∣ x + 3 ∣ + C

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

t an g e n t f (x) = x^{2} + 5 x - 2, at x = - 1

x \to 0 + lim (\frac{6}{x ^{2} - x})

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

\frac{\partial}{\partial x} ((2 x + 8 y)^{3})