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-45)

Lösung

\int x x - 45 d x

Lösung

\frac{2}{5} (x - 45)^{\frac{5}{2}} + 30 (x - 45)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x x - 45 d x

Wende U-Substitution an

= \int (u + 45) u d u

Multipliziere aus

(u + 45) u : u^{\frac{3}{2}} + 45 u

= \int u^{\frac{3}{2}} + 45 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 45 u d u

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

\int 45 u d u = 30 u^{\frac{3}{2}}

= \frac{2}{5} u^{\frac{5}{2}} + 30 u^{\frac{3}{2}}

Setze in

u = x - 45

ein

= \frac{2}{5} (x - 45)^{\frac{5}{2}} + 30 (x - 45)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{2}{5} (x - 45)^{\frac{5}{2}} + 30 (x - 45)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

integral of sin(pix)cos(2pix)

\int sin (π x) cos (2 π x) d x

integral of ((1+\sqrt[3]{x}))/(sqrt(x))

\int \frac{( 1 + 3 x )}{x} d x

integral of 6(x-4)^5

\int 6 (x - 4)^{5} d x

integral of x(1-x^4)^{3/2}

\int x (1 - x^{4})^{\frac{3}{2}} d x

integral of (e^{3x}+6)^3e^{2x}

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