integral of (1+3x)^2

Lösung

\int (1 + 3 x)^{2} d x

x + 3 x^{2} + 3 x^{3} + C

Schritte zur Lösung

\int (1 + 3 x)^{2} d x

Multipliziere aus

(1 + 3 x)^{2} : 1 + 6 x + 9 x^{2}

= \int 1 + 6 x + 9 x^{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 1 d x + \int 6 x d x + \int 9 x^{2} d x

\int 1 d x = x

\int 6 x d x = 3 x^{2}

\int 9 x^{2} d x = 3 x^{3}

= x + 3 x^{2} + 3 x^{3}

Füge eine Konstante zur Lösung hinzu

= x + 3 x^{2} + 3 x^{3} + C

n = 1 \sum \infty arctan (15 n)

t an g e n t f (x) = 6 x^{2} + 6, at x = - 2

d er i v a t i v e (3 x - 1) (x - 2)^{4}

\int \frac{x ^{2}}{x ^{2} + 18} d x

x \to 3 lim (\frac{x - 4}{x ^{2} - 9})