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Beliebt Rechnen >

integral of sqrt(x)(3+5x)

Lösung

\int x (3 + 5 x) d x

Lösung

2 x^{\frac{3}{2}} + 2 x^{\frac{5}{2}} + C

Schritte zur Lösung

\int x (3 + 5 x) d x

Multipliziere aus

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

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

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

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

= 2 x^{\frac{3}{2}} + 2 x^{\frac{5}{2}}

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

limit as x approaches 2 of 3f(x)+2g(x)(x)^2

x \to 2 lim (3 f (x) + 2 g (x) (x)^{2})

inverselaplace (2s^2+5s+5)/((s+1)^3)

in v erse l a pl a ce \frac{2 s ^{2} + 5 s + 5}{( s + 1 ) ^{3}}

tangent (5/x),\at x=4

t an g e n t (\frac{5}{x}), at x = 4

integral of 3e^x+5sin(x)

\int 3 e^{x} + 5 sin (x) d x

tangent y=(x^3-25x)^8,(5,0)

t an g e n t y = (x^{3} - 25 x)^{8}, (5, 0)