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Beliebt Rechnen >

integral of x(3x+10)^{49}

Lösung

\int x (3 x + 10)^{49} d x

Lösung

\frac{1}{9} (\frac{( 3 x + 10 ) ^{51}}{51} - \frac{( 3 x + 10 ) ^{50}}{5}) + C

Schritte zur Lösung

\int x (3 x + 10)^{49} d x

Wende U-Substitution an

= \int \frac{u ^{49} ( u - 10 )}{9} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{9} \cdot \int u^{49} (u - 10) d u

Multipliziere aus

u^{49} (u - 10) : u^{50} - 10 u^{49}

= \frac{1}{9} \cdot \int u^{50} - 10 u^{49} 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

= \frac{1}{9} (\int u^{50} d u - \int 10 u^{49} d u)

\int u^{50} d u = \frac{u ^{51}}{51}

\int 10 u^{49} d u = \frac{u ^{50}}{5}

= \frac{1}{9} (\frac{u ^{51}}{51} - \frac{u ^{50}}{5})

Setze in

u = 3 x + 10

ein

= \frac{1}{9} (\frac{( 3 x + 10 ) ^{51}}{51} - \frac{( 3 x + 10 ) ^{50}}{5})

Füge eine Konstante zur Lösung hinzu

= \frac{1}{9} (\frac{( 3 x + 10 ) ^{51}}{51} - \frac{( 3 x + 10 ) ^{50}}{5}) + C

Graph

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