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Beliebt Rechnen >

integral of (5x^2-15x+45/4)^{1/2}

Lösung

\int (5 x^{2} - 15 x + \frac{45}{4})^{\frac{1}{2}} d x

Lösung

\frac{5 ^{\frac{1}{2}}}{2} (x^{2} - 3 x) + C

Schritte zur Lösung

\int (5 x^{2} - 15 x + \frac{45}{4})^{\frac{1}{2}} d x

Vereinfache

(5 x^{2} - 15 x + \frac{45}{4})^{\frac{1}{2}} : \frac{5 ^{\frac{1}{2}}}{2} (2 x - 3)

= \int \frac{5 ^{\frac{1}{2}}}{2} (2 x - 3) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{5 ^{\frac{1}{2}}}{2} \cdot \int 2 x - 3 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

= \frac{5 ^{\frac{1}{2}}}{2} (\int 2 x d x - \int 3 d x)

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

\int 3 d x = 3 x

= \frac{5 ^{\frac{1}{2}}}{2} (x^{2} - 3 x)

Füge eine Konstante zur Lösung hinzu

= \frac{5 ^{\frac{1}{2}}}{2} (x^{2} - 3 x) + C

Graph

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