integral of (x^2-4x+5)^2

Lösung

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

\frac{x ^{5}}{5} - 2 x^{4} + \frac{26 x ^{3}}{3} - 20 x^{2} + 25 x + C

Schritte zur Lösung

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

Multipliziere aus

(x^{2} - 4 x + 5)^{2} : x^{4} - 8 x^{3} + 26 x^{2} - 40 x + 25

= \int x^{4} - 8 x^{3} + 26 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 x^{4} d x - \int 8 x^{3} d x + \int 26 x^{2} d x - \int 40 x d x + \int 25 d x

\int x^{4} d x = \frac{x ^{5}}{5}

\int 8 x^{3} d x = 2 x^{4}

\int 26 x^{2} d x = \frac{26 x ^{3}}{3}

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

\int 25 d x = 25 x

= \frac{x ^{5}}{5} - 2 x^{4} + \frac{26 x ^{3}}{3} - 20 x^{2} + 25 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{5}}{5} - 2 x^{4} + \frac{26 x ^{3}}{3} - 20 x^{2} + 25 x + C

d er i v a t i v e (x + 2)^{\frac{2}{3}}

t an g e n t y = \frac{( x - 2 )}{( x - 3 )}

l a pl a ce t r an s f or m 6 e^{5 t} cos (2 t) - e^{- 7 t}

\int_{1}^{1000} \frac{1}{x ^{3}} d x

d er i v a t i v e \frac{v ^{3} + 1}{v}