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Beliebt Rechnen >

integral of (2x+1)/(sqrt(x-2))

Lösung

\int \frac{2 x + 1}{x - 2} d x

Lösung

\frac{4}{3} (x - 2)^{\frac{3}{2}} + 10 x - 2 + C

Schritte zur Lösung

\int \frac{2 x + 1}{x - 2} d x

Multipliziere aus

\frac{2 x + 1}{x - 2} : \frac{2 x}{x - 2} + \frac{1}{x - 2}

= \int \frac{2 x}{x - 2} + \frac{1}{x - 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 \frac{2 x}{x - 2} d x + \int \frac{1}{x - 2} d x

\int \frac{2 x}{x - 2} d x = 4 (\frac{1}{3} (x - 2)^{\frac{3}{2}} + 2 x - 2)

\int \frac{1}{x - 2} d x = 2 x - 2

= 4 (\frac{1}{3} (x - 2)^{\frac{3}{2}} + 2 x - 2) + 2 x - 2

Vereinfache

4 (\frac{1}{3} (x - 2)^{\frac{3}{2}} + 2 x - 2) + 2 x - 2 : \frac{4}{3} (x - 2)^{\frac{3}{2}} + 10 x - 2

= \frac{4}{3} (x - 2)^{\frac{3}{2}} + 10 x - 2

Füge eine Konstante zur Lösung hinzu

= \frac{4}{3} (x - 2)^{\frac{3}{2}} + 10 x - 2 + C

Graph

Beliebte Beispiele

y^{^{'}} = y (y^{3} - 1)

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