integral of (12x+5)^2

Lösung

\int (12 x + 5)^{2} d x

48 x^{3} + 60 x^{2} + 25 x + C

Schritte zur Lösung

\int (12 x + 5)^{2} d x

Multipliziere aus

(12 x + 5)^{2} : 144 x^{2} + 120 x + 25

= \int 144 x^{2} + 120 x + 25 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 144 x^{2} d x + \int 120 x d x + \int 25 d x

\int 144 x^{2} d x = 48 x^{3}

\int 120 x d x = 60 x^{2}

\int 25 d x = 25 x

= 48 x^{3} + 60 x^{2} + 25 x

Füge eine Konstante zur Lösung hinzu

= 48 x^{3} + 60 x^{2} + 25 x + C

n = 1 \sum \infty n 6

t an g e n t sin (9 x) + cos (2 x)

d er i v a t i v e y = (2 x^{4} + 1)^{2}

t an g e n t f (x) = \frac{4 x}{x ^{2} + 1}, (0, 0)

\int_{1}^{3} \frac{1}{( x - 1 ) ^{\frac{3}{2}}} d x