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Beliebt Rechnen >

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

Lösung

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

Lösung

x - 3 arctan (\frac{1}{3} (x + 1)) + C

Schritte zur Lösung

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

Lange Division

\frac{( x + 1 ) ^{2}}{x ^{2} + 2 x + 4} : 1 - \frac{3}{x ^{2} + 2 x + 4}

= \int 1 - \frac{3}{x ^{2} + 2 x + 4} 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 1 d x - \int \frac{3}{x ^{2} + 2 x + 4} d x

\int 1 d x = x

\int \frac{3}{x ^{2} + 2 x + 4} d x = 3 arctan (\frac{1}{3} (x + 1))

= x - 3 arctan (\frac{1}{3} (x + 1))

Füge eine Konstante zur Lösung hinzu

= x - 3 arctan (\frac{1}{3} (x + 1)) + C

Graph

Beliebte Beispiele

integral of x/(sqrt(4+x^4))

\int \frac{x}{4 + x ^{4}} d x

integral of (x+2)/(x^{1/2)}

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

integral of (x^3+x)3^{(x^4+2x^2)}

\int (x^{3} + x) 3^{(x^{4} + 2 x^{2})} d x

integral of sin(2t)e^{-st}

\int sin (2 t) e^{- s t} d t

integral of x/(x^6)

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