integral of xsqrt(x-10)

Lösung

\int x x - 10 d x

\frac{2}{5} (x - 10)^{\frac{5}{2}} + \frac{20}{3} (x - 10)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x x - 10 d x

Wende U-Substitution an

= \int (u + 10) u d u

Multipliziere aus

(u + 10) u : u^{\frac{3}{2}} + 10 u

= \int u^{\frac{3}{2}} + 10 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 10 u d u

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

\int 10 u d u = \frac{20}{3} u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} + \frac{20}{3} u^{\frac{3}{2}}

Setze in

u = x - 10

ein

= \frac{2}{5} (x - 10)^{\frac{5}{2}} + \frac{20}{3} (x - 10)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} (x - 10)^{\frac{5}{2}} + \frac{20}{3} (x - 10)^{\frac{3}{2}} + C

in v erse l a pl a ce \frac{3}{s} + \frac{16}{s ( s + 1 )}

\int_{1}^{e^{2}} \frac{ln ( x )}{x ^{2}} d x

\frac{\partial}{\partial x} (\frac{a - b ^{2}}{x - c ^{2}})

\frac{d}{d x} (5 - \frac{4}{x})

d er i v a t i v e \frac{- u ^{2} + 7}{( u ^{2} + 7 ) ^{2}}