integral of (xsqrt(x+6))

Lösung

\int (x x + 6) d x

\frac{2}{5} (x + 6)^{\frac{5}{2}} - 4 (x + 6)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x x + 6 d x

Wende U-Substitution an

= \int (u - 6) u d u

Multipliziere aus

(u - 6) u : u^{\frac{3}{2}} - 6 u

= \int u^{\frac{3}{2}} - 6 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 6 u d u

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

\int 6 u d u = 4 u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} - 4 u^{\frac{3}{2}}

Setze in

u = x + 6

ein

= \frac{2}{5} (x + 6)^{\frac{5}{2}} - 4 (x + 6)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} (x + 6)^{\frac{5}{2}} - 4 (x + 6)^{\frac{3}{2}} + C

\int 7 cos (θ) cos^{5} (sin (θ)) d θ

d er i v a t i v e arccos (7 x^{3})

\frac{\partial}{\partial x} (2 y e^{x^{2} + y^{2}})

\frac{d}{d x} (ln (1 + \frac{5}{x}))

t \to \frac{π}{3} lim (cos (t) + 2)