de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (xsqrt(x-3))

Lösung

\int (x x - 3) d x

Lösung

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

Schritte zur Lösung

\int x x - 3 d x

Wende U-Substitution an

= \int (u + 3) u d u

Multipliziere aus

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

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

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

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

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

Setze in

u = x - 3

ein

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 1/(x-x^{1/3)}

\int \frac{1}{x - x ^{\frac{1}{3}}} d x

integral of x^2cos(x^3)3sin(x^3)

\int x^{2} cos (x^{3}) 3 sin (x^{3}) d x

integral of (2x^2+1)sin(x)

\int (2 x^{2} + 1) sin (x) d x

integral of (5t^3+2t^2+t)

\int (5 t^{3} + 2 t^{2} + t) d t

integral of csc^3(θ)

\int csc^{3} (θ) d θ