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Beliebt Rechnen >

integral of (2+y^2)e^y

Lösung

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

Lösung

e^{y} y^{2} - 2 e^{y} y + 4 e^{y} + C

Schritte zur Lösung

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

Wende die partielle Integration an

= (2 + y^{2}) e^{y} - \int 2 y e^{y} d y

\int 2 y e^{y} d y = 2 (e^{y} y - e^{y})

= (2 + y^{2}) e^{y} - 2 (e^{y} y - e^{y})

Vereinfache

(2 + y^{2}) e^{y} - 2 (e^{y} y - e^{y}) : e^{y} y^{2} - 2 e^{y} y + 4 e^{y}

= e^{y} y^{2} - 2 e^{y} y + 4 e^{y}

Füge eine Konstante zur Lösung hinzu

= e^{y} y^{2} - 2 e^{y} y + 4 e^{y} + C

Graph

Beliebte Beispiele

integral of (4x)/(x-1)

\int \frac{4 x}{x - 1} d x

integral of e^{1/x}x^{-2}

\int e^{\frac{1}{x}} x^{- 2} d x

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

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

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\int (\frac{x ^{3} + 4 x ^{2} + 8 x + 5}{x ^{2} + 2 x + 1}) d x

integral of 1/(sqrt(x^2)-4)

\int \frac{1}{x ^{2} - 4} d x