integral of (x-1)^2-4

Lösung

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

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

Schritte zur Lösung

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

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

\int 4 d x = 4 x

= \frac{x ^{3}}{3} - x^{2} + x - 4 x

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

\int (x + 1) (x + 2) d x

x \to 1 lim (\frac{1}{x + 1})

a re a f (x) = x^{2}, x = 0, x = 2

d er i v a t i v e \frac{6 e ^{s} s - 5 e ^{s}}{( 6 s + 1 ) ^{2}}

\int \frac{x ^{3} + 22}{x ^{2} + 7 x + 12} d x