integral of (x^2-2)sqrt(x^3-6x+3)

Lösung

\int (x^{2} - 2) x^{3} - 6 x + 3 d x

\frac{2}{9} (x^{3} - 6 x + 3)^{\frac{3}{2}} + C

Schritte zur Lösung

\int (x^{2} - 2) x^{3} - 6 x + 3 d x

Wende U-Substitution an

= \int \frac{u}{3} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int u d u

Wende die Potenzregel an

= \frac{1}{3} \cdot \frac{2}{3} u^{\frac{3}{2}}

Setze in

u = x^{3} - 6 x + 3

ein

= \frac{1}{3} \cdot \frac{2}{3} (x^{3} - 6 x + 3)^{\frac{3}{2}}

Vereinfache

\frac{1}{3} \cdot \frac{2}{3} (x^{3} - 6 x + 3)^{\frac{3}{2}} : \frac{2}{9} (x^{3} - 6 x + 3)^{\frac{3}{2}}

= \frac{2}{9} (x^{3} - 6 x + 3)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{9} (x^{3} - 6 x + 3)^{\frac{3}{2}} + C

\int 3 x e^{7 x^{2}} d x

f (x) = 16 cos (2 x)

\int csc^{2} (x) d x

f (x) = tan (\frac{π x}{2})

x \to 0 lim (\frac{3 x ^{2} - 4 x}{x})