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Beliebt Rechnen >

integral of 8(x+1)In(x+1)

Lösung

\int 8 (x + 1) I n (x + 1) d x

Lösung

8 I n (x + x^{2} + \frac{x ^{3}}{3}) + C

Schritte zur Lösung

\int 8 (x + 1) I n (x + 1) d x

Entferne die Konstante:

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

= 8 I n \cdot \int (1 + x) (1 + x) d x

Vereinfache

(1 + x) (1 + x) : (1 + x)^{2}

= 8 I n \cdot \int (1 + x)^{2} d x

Multipliziere aus

(1 + x)^{2} : 1 + 2 x + x^{2}

= 8 I n \cdot \int 1 + 2 x + x^{2} d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 8 I n (\int 1 d x + \int 2 x d x + \int x^{2} d x)

\int 1 d x = x

\int 2 x d x = x^{2}

\int x^{2} d x = \frac{x ^{3}}{3}

= 8 I n (x + x^{2} + \frac{x ^{3}}{3})

Füge eine Konstante zur Lösung hinzu

= 8 I n (x + x^{2} + \frac{x ^{3}}{3}) + C

Graph

Beliebte Beispiele

sum from n=0 to infinity of z^{3n}

n = 0 \sum \infty z^{3 n}

limit as x approaches infinity of (a_{n+1})/(a_{n)}

x \to \infty lim (\frac{a _{n + 1}}{a _{n}})

(dr)/(dt)= 1/(t+1),r(0)=1

\frac{d r}{d t} = \frac{1}{t + 1}, r (0) = 1

(1+x^2)y^'+1+2xy=0

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

integral of x^2(3-e^{x^3})

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