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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

Schritte zur Lösung

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

Vereinfache

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

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

Multipliziere aus

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

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

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

\int 2 d x = 2 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{x ^{2}}{2} + 2 x + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{2}}{2} + 2 x + ln ∣ x ∣ + C

Graph

Beliebte Beispiele

derivative of xcos(x-picos(x)+2sin(x))

\frac{d}{d x} (x cos (x) - π cos (x) + 2 sin (x))

6y^{''}+y^'-y=0

6 y^{^{''}} + y^{^{'}} - y = 0

integral from 0 to pi/3 of cos^3(x)

\int_{0}^{\frac{π}{3}} cos^{3} (x) d x

(xy^2+x^3)dx+(y^3+x^2y)dy=0

(x y^{2} + x^{3}) d x + (y^{3} + x^{2} y) d y = 0

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

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