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Beliebt Rechnen >

integral of (x^2-2x+3)^2(x+1)

Lösung

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

Lösung

\frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} - \frac{2 x ^{3}}{3} - \frac{3 x ^{2}}{2} + 9 x + C

Schritte zur Lösung

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

Multipliziere aus

(x^{2} - 2 x + 3)^{2} (x + 1) : x^{5} - 3 x^{4} + 6 x^{3} - 2 x^{2} - 3 x + 9

= \int x^{5} - 3 x^{4} + 6 x^{3} - 2 x^{2} - 3 x + 9 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^{5} d x - \int 3 x^{4} d x + \int 6 x^{3} d x - \int 2 x^{2} d x - \int 3 x d x + \int 9 d x

\int x^{5} d x = \frac{x ^{6}}{6}

\int 3 x^{4} d x = \frac{3 x ^{5}}{5}

\int 6 x^{3} d x = \frac{3 x ^{4}}{2}

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

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

\int 9 d x = 9 x

= \frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} - \frac{2 x ^{3}}{3} - \frac{3 x ^{2}}{2} + 9 x

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{6}}{6} - \frac{3 x ^{5}}{5} + \frac{3 x ^{4}}{2} - \frac{2 x ^{3}}{3} - \frac{3 x ^{2}}{2} + 9 x + C

Graph

Beliebte Beispiele

integral of x^3e^{2x}

\int x^{3} e^{2 x} d x

sum from n=1 to infinity of (n^5)/(2^n)

n = 1 \sum \infty \frac{n ^{5}}{2 ^{n}}

laplacetransform F(x)=sin(2x)-2xcos(2x)

l a pl a ce t r an s f or m F (x) = sin (2 x) - 2 x cos (2 x)

integral of 2ye^{xy}

\int 2 y e^{x y} d y

slopeintercept (10,6),(-5,-3)

s l o p e in t erce pt (10, 6), (- 5, - 3)