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Beliebt Rechnen >

integral of ln(x)+x

Lösung

\int ln (x) + x d x

Lösung

x ln (x) - x + \frac{x ^{2}}{2} + C

Schritte zur Lösung

\int ln (x) + x 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

= \int ln (x) d x + \int x d x

\int ln (x) d x = x ln (x) - x

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

= x ln (x) - x + \frac{x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= x ln (x) - x + \frac{x ^{2}}{2} + C

Graph

Beliebte Beispiele

integral of sin^3(18x)

\int sin^{3} (18 x) d x

derivative g(t)=(9t+5)^2(5t-6)^{-3}

d er i v a t i v e g (t) = (9 t + 5)^{2} (5 t - 6)^{- 3}

(3x+2)+(3y-3)y^'=0

(3 x + 2) + (3 y - 3) y^{^{'}} = 0

integral of y(y+1)e^{-2y}

\int y (y + 1) e^{- 2 y} d y

integral of e+e^{3x}

\int e + e^{3 x} d x