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Beliebt Rechnen >

integral of (xsqrt(x+3))

Lösung

\int (x x + 3) d x

Lösung

\frac{2}{5} (x + 3)^{\frac{5}{2}} - 2 (x + 3)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x x + 3 d x

Wende U-Substitution an

= \int (u - 3) u d u

Multipliziere aus

(u - 3) u : u^{\frac{3}{2}} - 3 u

= \int u^{\frac{3}{2}} - 3 u d u

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int u^{\frac{3}{2}} d u - \int 3 u d u

\int u^{\frac{3}{2}} d u = \frac{2}{5} u^{\frac{5}{2}}

\int 3 u d u = 2 u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} - 2 u^{\frac{3}{2}}

Setze in

u = x + 3

ein

= \frac{2}{5} (x + 3)^{\frac{5}{2}} - 2 (x + 3)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} (x + 3)^{\frac{5}{2}} - 2 (x + 3)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x^4+y^4+3x^2y^3)

\frac{\partial}{\partial x} (x^{4} + y^{4} + 3 x^{2} y^{3})

fläche 13+2x-x^2,3x+1

a re a 13 + 2 x - x^{2}, 3 x + 1

derivative f(x)=(x+1)^{2x}

d er i v a t i v e f (x) = (x + 1)^{2 x}

wurzeln von x/a

roo t s \frac{x}{a}

tangent x/y =sin((pixy)/2),(1,1)

t an g e n t \frac{x}{y} = sin (\frac{π x y}{2}), (1, 1)