integral of |x|-x^2-2

Lösung

\int ∣ x ∣ - x^{2} - 2 d x

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

Schritte zur Lösung

\int ∣ 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 ∣ x ∣ d x - \int x^{2} d x - \int 2 d x

\int ∣ x ∣ d x = \frac{x ∣ x ∣}{2}

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

\int 2 d x = 2 x

= \frac{x ∣ x ∣}{2} - \frac{x ^{3}}{3} - 2 x

Füge eine Konstante zur Lösung hinzu

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

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

\int t^{2} + 5 d t

\int \frac{4 ( x ^{2} + 1 )}{x ( x ^{2} + 4 )} d x

\int \frac{1}{cos ( 5 x )} d x

\int \frac{2}{4 x} d x