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Beliebt Rechnen >

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

Lösung

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

Lösung

ln 1 + x^{2} + x + C

Schritte zur Lösung

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

\frac{( 1 + x ) ^{2}}{1 + x ^{2}} = \frac{2 x}{1 + x ^{2}} + 1

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

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

\int 1 d x = x

= ln 1 + x^{2} + x

Füge eine Konstante zur Lösung hinzu

= ln 1 + x^{2} + x + C

Graph

Beliebte Beispiele

(dy)/(dt)+3y=13sin(2t)

integral of (2x+1)/(x(x+2)^3)

2xydx+(x^2-y)dy=0

(\partial)/(\partial x)((64)/(x^2))

(\partial)/(\partial x)(ln(sqrt(1+x^2)))