integral of x^4-8x^3+26x^2-40x+25

Lösung

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

x \to 7 lim (\frac{x - 7}{x - 7})

x \to 0.5 + lim (3 x)

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

x \to 1 lim (\frac{1}{( x - 1 ) ^{2}})

\int_{0}^{7} x e^{- 2 x} d x