de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of x^3sqrt(x^2+25)

Lösung

\int x^{3} x^{2} + 25 d x

Lösung

\frac{1}{5} (x^{2} + 25)^{\frac{5}{2}} - \frac{25}{3} (x^{2} + 25)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{3} x^{2} + 25 d x

Wende U-Substitution an

= \int (u^{2} - 25) u^{2} d u

Multipliziere aus

(u^{2} - 25) u^{2} : u^{4} - 25 u^{2}

= \int u^{4} - 25 u^{2} 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^{4} d u - \int 25 u^{2} d u

\int u^{4} d u = \frac{u ^{5}}{5}

\int 25 u^{2} d u = \frac{25 u ^{3}}{3}

= \frac{u ^{5}}{5} - \frac{25 u ^{3}}{3}

Setze in

u = x^{2} + 25

ein

= \frac{( x ^{2} + 25 ) ^{5}}{5} - \frac{25 ( x ^{2} + 25 ) ^{3}}{3}

Vereinfache

\frac{( x ^{2} + 25 ) ^{5}}{5} - \frac{25 ( x ^{2} + 25 ) ^{3}}{3} : \frac{1}{5} (x^{2} + 25)^{\frac{5}{2}} - \frac{25}{3} (x^{2} + 25)^{\frac{3}{2}}

= \frac{1}{5} (x^{2} + 25)^{\frac{5}{2}} - \frac{25}{3} (x^{2} + 25)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} (x^{2} + 25)^{\frac{5}{2}} - \frac{25}{3} (x^{2} + 25)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)(2(xe^{x/2+y}+1))

\frac{\partial}{\partial x} (2 (x e^{\frac{x}{2} + y} + 1))

derivative of 2e^x+3x-ln(x)

\frac{d}{d x} (2 e^{x} + 3 x - ln (x))

integral of-1/2 sin(2x)

\int - \frac{1}{2} sin (2 x) d x

limit as x approaches 80 of 82-x

x \to 80 lim (82 - x)

integral of 2sin(pix)

\int 2 sin (π x) d x