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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 cos^2(θ)sin(2θ)

\int cos^{2} (θ) sin (2 θ) d θ

integral of (2x+3)/(x^2+2x-3)

\int \frac{2 x + 3}{x ^{2} + 2 x - 3} d x

integral of (e^{4x})/(e^{4x)-6}

\int \frac{e ^{4 x}}{e ^{4 x} - 6} d x

integral of 2/((2x-5)ln(2x-5))

\int \frac{2}{( 2 x - 5 ) ln ( 2 x - 5 )} d x

integral of (7x)/(1+x^2)

\int \frac{7 x}{1 + x ^{2}} d x