integral of (x+6)^2

Lösung

\int (x + 6)^{2} d x

\frac{x ^{3}}{3} + 6 x^{2} + 36 x + C

Schritte zur Lösung

\int (x + 6)^{2} d x

Multipliziere aus

(x + 6)^{2} : x^{2} + 12 x + 36

= \int x^{2} + 12 x + 36 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 12 x d x + \int 36 d x

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

\int 12 x d x = 6 x^{2}

\int 36 d x = 36 x

= \frac{x ^{3}}{3} + 6 x^{2} + 36 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} + 6 x^{2} + 36 x + C

\int sin (x) \cdot sin (2 \cdot x) d x

d er i v a t i v e \frac{x - x}{x ^{\frac{1}{4}}}

d er i v a t i v e \frac{5}{2} x^{\frac{5}{2}}

t an g e n t f (x) = 2 x^{4} - 10 x^{2}, at x = - 2

\frac{d}{d x} (ln (x - \frac{π}{2}))