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Beliebt Rechnen >

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

Lösung

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

Lösung

x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Schritte zur Lösung

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

Multipliziere aus

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

= \int 1 + 2 x + 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 1 d x + \int 2 x d x + \int x d x

\int 1 d x = x

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

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

= x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= x + \frac{4}{3} x^{\frac{3}{2}} + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

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

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

derivative of-(2x/((x+1)^2(x-1)^2))

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

integral of [5x^4+10cos(x)]

\int [5 x^{4} + 10 cos (x)] d x

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

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

(\partial)/(\partial x)(3(x-6)^3)

\frac{\partial}{\partial x} (3 (x - 6)^{3})