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Beliebt Rechnen >

integral of ysqrt(y-3)

Lösung

\int y y - 3 d y

Lösung

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

Schritte zur Lösung

\int y y - 3 d y

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 = y - 3

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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\int 9 x x d x

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\int \frac{7}{16 - 4 t ^{2}} d t

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\int 4 x x + 1 d x