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Beliebt Rechnen >

integral from 1 to n of xln(x)

Lösung

\int_{1}^{n} x ln (x) d x

Lösung

\frac{n ^{2} ln ( n )}{2} + \frac{- n ^{2} + 1}{4}

Schritte zur Lösung

\int_{1}^{n} x ln (x) d x

Wende die partielle Integration an

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{1}^{n}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{1}^{n}

Berechne die Grenzen:

\frac{1}{2} n^{2} ln (n) - \frac{n ^{2}}{4} + \frac{1}{4}

= \frac{1}{2} n^{2} ln (n) - \frac{n ^{2}}{4} + \frac{1}{4}

Vereinfache

= \frac{n ^{2} ln ( n )}{2} + \frac{- n ^{2} + 1}{4}

Beliebte Beispiele

integral of (4-x^2)^{3/2}

\int (4 - x^{2})^{\frac{3}{2}} d x

\frac{d y}{d t} = 5 y

integral of x+x

\int x + x d x

limit as x approaches infinity of (e^{2x})/(e^{2x)+1}

x \to \infty lim (\frac{e ^{2 x}}{e ^{2 x} + 1})

derivative f(x)=e^8

d er i v a t i v e f (x) = e^{8}