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+49)

Lösung

\int x^{3} x^{2} + 49 d x

Lösung

\frac{1}{5} (x^{2} + 49)^{\frac{5}{2}} - \frac{49}{3} (x^{2} + 49)^{\frac{3}{2}} + C

Schritte zur Lösung

\int x^{3} x^{2} + 49 d x

Wende U-Substitution an

= \int (u^{2} - 49) u^{2} d u

Multipliziere aus

(u^{2} - 49) u^{2} : u^{4} - 49 u^{2}

= \int u^{4} - 49 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 49 u^{2} d u

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

\int 49 u^{2} d u = \frac{49 u ^{3}}{3}

= \frac{u ^{5}}{5} - \frac{49 u ^{3}}{3}

Setze in

u = x^{2} + 49

ein

= \frac{( x ^{2} + 49 ) ^{5}}{5} - \frac{49 ( x ^{2} + 49 ) ^{3}}{3}

Vereinfache

\frac{( x ^{2} + 49 ) ^{5}}{5} - \frac{49 ( x ^{2} + 49 ) ^{3}}{3} : \frac{1}{5} (x^{2} + 49)^{\frac{5}{2}} - \frac{49}{3} (x^{2} + 49)^{\frac{3}{2}}

= \frac{1}{5} (x^{2} + 49)^{\frac{5}{2}} - \frac{49}{3} (x^{2} + 49)^{\frac{3}{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{1}{5} (x^{2} + 49)^{\frac{5}{2}} - \frac{49}{3} (x^{2} + 49)^{\frac{3}{2}} + C

Graph

Beliebte Beispiele

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

\int \frac{2 x ^{2} + 1}{2 x ^{2} + x} d x

integral of x^3sqrt(9+x^4)

\int x^{3} 9 + x^{4} d x

integral of 1/3 x^3cos(x^4+2)

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

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

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

integral of ((a+bx^5))/(sqrt(6ax+bx^6))

\int \frac{( a + b x ^{5} )}{6 a x + b x ^{6}} d x