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Beliebt Rechnen >

integral of (x^2+2xy+y^2)

Lösung

\int (x^{2} + 2 x y + y^{2}) d x

Lösung

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

Schritte zur Lösung

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

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

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

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

= y^{2} x + \frac{x ^{3}}{3} + y x^{2}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of (2x-3)/(3x^2+4x-7)

\int \frac{2 x - 3}{3 x ^{2} + 4 x - 7} d x

integral of ln(sqrt(x^2-1))

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

integral of ((x^2))/(sqrt(x))

\int \frac{( x ^{2} )}{x} d x

integral of (6x+9)ln(x+3)

\int (6 x + 9) ln (x + 3) d x

integral of 4/(5x)

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