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+15)

Lösung

\int x^{3} x^{2} + 15 d x

Lösung

\frac{1}{5} (x^{2} + 15)^{\frac{5}{2}} - 5 (x^{2} + 15)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{3} x^{2} + 15 d x

Wende U-Substitution an

= \int (u^{2} - 15) u^{2} d u

Multipliziere aus

(u^{2} - 15) u^{2} : u^{4} - 15 u^{2}

= \int u^{4} - 15 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 15 u^{2} d u

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

\int 15 u^{2} d u = 5 u^{3}

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

Setze in

u = x^{2} + 15

ein

= \frac{( x ^{2} + 15 ) ^{5}}{5} - 5 (x^{2} + 15)^{3}

Vereinfache

\frac{( x ^{2} + 15 ) ^{5}}{5} - 5 (x^{2} + 15)^{3} : \frac{1}{5} (x^{2} + 15)^{\frac{5}{2}} - 5 (x^{2} + 15)^{\frac{3}{2}}

= \frac{1}{5} (x^{2} + 15)^{\frac{5}{2}} - 5 (x^{2} + 15)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} (x^{2} + 15)^{\frac{5}{2}} - 5 (x^{2} + 15)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

sum from n=1 to infinity of 1/(2^n(n+1))

n = 1 \sum \infty \frac{1}{2 ^{n} ( n + 1 )}

limit as x approaches 9 of (4x)/(x-9)

x \to 9 lim (\frac{4 x}{x - 9})

y^'*(x-1)+y*(x-2)=0

y^{^{'}} \cdot (x - 1) + y \cdot (x - 2) = 0

inverselaplace 1/((s+2)(s+3))

in v erse l a pl a ce \frac{1}{( s + 2 ) ( s + 3 )}

derivative of e^{4x+1}

\frac{d}{d x} (e^{4 x + 1})