integral of (2x^2y-3xy^2+2)

Lösung

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

2 y + x^{2} y^{2} - x y^{3} + C

Schritte zur Lösung

\int 2 x^{2} y - 3 x y^{2} + 2 d y

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 2 d y + \int 2 x^{2} y d y - \int 3 x y^{2} d y

\int 2 d y = 2 y

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

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

= 2 y + x^{2} y^{2} - x y^{3}

Füge eine Konstante zur Lösung hinzu

= 2 y + x^{2} y^{2} - x y^{3} + C

\int x^{2} csc (x^{3} - 2) cot (x^{3} - 2) d x

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