integral of (xln(x))/x

Lösung

\int \frac{x ln ( x )}{x} d x

x ln (x) - x + C

Schritte zur Lösung

\int \frac{x ln ( x )}{x} d x

Wende U-Substitution an

= \int e^{u} u d u

Wende die partielle Integration an

= e^{u} u - \int e^{u} d u

\int e^{u} d u = e^{u}

= e^{u} u - e^{u}

Setze in

u = ln (x)

ein

= e^{l n (x)} ln (x) - e^{l n (x)}

Vereinfache

e^{l n (x)} ln (x) - e^{l n (x)} : x ln (x) - x

= x ln (x) - x

Füge eine Konstante zur Lösung hinzu

= x ln (x) - x + C

t an g e n t f (x) = \frac{1}{x ^{5}}, (2, \frac{1}{32})

d er i v a t i v e f (t) = 2 t^{2} - t

y^{^{'}} + \frac{1}{x + 1} y = x^{- 2}

t an g e n t f (x) = (3 x - 2) (x + 4), (1, 5)

\frac{\partial}{\partial y} (x \cdot cos (y) \cdot sin (z))