integral of (4x-5)^2

Lösung

\int (4 x - 5)^{2} d x

\frac{16 x ^{3}}{3} - 20 x^{2} + 25 x + C

Schritte zur Lösung

\int (4 x - 5)^{2} d x

Multipliziere aus

(4 x - 5)^{2} : 16 x^{2} - 40 x + 25

= \int 16 x^{2} - 40 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 16 x^{2} d x - \int 40 x d x + \int 25 d x

\int 16 x^{2} d x = \frac{16 x ^{3}}{3}

\int 40 x d x = 20 x^{2}

\int 25 d x = 25 x

= \frac{16 x ^{3}}{3} - 20 x^{2} + 25 x

Füge eine Konstante zur Lösung hinzu

= \frac{16 x ^{3}}{3} - 20 x^{2} + 25 x + C