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Beliebt Rechnen >

integral of (x(y^2-5y+6))/(x^2+1)

Lösung

\int \frac{x ( y ^{2} - 5 y + 6 )}{x ^{2} + 1} d x

Lösung

(6 + y^{2} - 5 y) \frac{1}{2} ln 1 + x^{2} + C

Schritte zur Lösung

\int \frac{x ( y ^{2} - 5 y + 6 )}{x ^{2} + 1} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= (6 + y^{2} - 5 y) \cdot \int \frac{x}{1 + x ^{2}} d x

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

= (6 + y^{2} - 5 y) \frac{1}{2} ln 1 + x^{2}

Füge eine Konstante zur Lösung hinzu

= (6 + y^{2} - 5 y) \frac{1}{2} ln 1 + x^{2} + C

Graph

Beliebte Beispiele

limit as x approaches 5 of in(x^2-25)

x \to 5 lim (in (x^{2} - 25))

derivative of arccsc(-5x^2)

\frac{d}{d x} (arccsc (- 5 x^{2}))

integral of (3x-5)/(x^2-4x+3)

\int \frac{3 x - 5}{x ^{2} - 4 x + 3} d x

integral of x^3+2x^2-x+k

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

limit as (x,y) approaches (2,1) of (x-2y)/(x^3-8y^3)

(x, y) \to (2, 1) lim (\frac{x - 2 y}{x ^{3} - 8 y ^{3}})