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Beliebt Rechnen >

integral of ((y-2)^2)/(sqrt(y))

Lösung

\int \frac{( y - 2 ) ^{2}}{y} d y

Lösung

\frac{2}{5} y^{\frac{5}{2}} - \frac{8}{3} y^{\frac{3}{2}} + 8 y + C

Schritte zur Lösung

\int \frac{( y - 2 ) ^{2}}{y} d y

Multipliziere aus

\frac{( y - 2 ) ^{2}}{y} : y^{\frac{3}{2}} - 4 y + \frac{4}{y}

= \int y^{\frac{3}{2}} - 4 y + \frac{4}{y} d y

Wende die Summenregel an:

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

= \int y^{\frac{3}{2}} d y - \int 4 y d y + \int \frac{4}{y} d y

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

\int 4 y d y = \frac{8}{3} y^{\frac{3}{2}}

\int \frac{4}{y} d y = 8 y

= \frac{2}{5} y^{\frac{5}{2}} - \frac{8}{3} y^{\frac{3}{2}} + 8 y

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} y^{\frac{5}{2}} - \frac{8}{3} y^{\frac{3}{2}} + 8 y + C

Graph

Beliebte Beispiele

tangent 100x^2+400x+5000

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\frac{d}{d x} (ln (4 + ln (x)))

(\partial)/(\partial x)(axln(ax))

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