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Beliebt Rechnen >

integral of sqrt(x^4+2x^2+1)

Lösung

\int x^{4} + 2 x^{2} + 1 d x

Lösung

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

Schritte zur Lösung

\int x^{4} + 2 x^{2} + 1 d x

Faktorisiere

x^{4} + 2 x^{2} + 1 : (x^{2} + 1)^{2}

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

(x^{2} + 1)^{2} = ((x^{2} + 1)),

angenommen

(x^{2} + 1) \geq 0

= \int x^{2} + 1 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^{2} d x + \int 1 d x

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

\int 1 d x = x

= \frac{x ^{3}}{3} + x

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 5^{2x^3}2x^2

\int 5^{2 x^{3}} 2 x^{2} d x

integral of 6xe^{6x}

\int 6 x e^{6 x} d x

integral of sqrt(16-2x)

\int 16 - 2 x d x

integral of 3/(sqrt(9-25x^2))

\int \frac{3}{9 - 25 x ^{2}} d x

integral of (1/(sqrt(x^2+1)))^3

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