integral from sqrt(x) to 2 of ln(t)

Lösung

\int_{x}^{2} ln (t) d t

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

Schritte zur Lösung

\int_{x}^{2} ln (t) d t

Wende die partielle Integration an

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

\int 1 d t = t

= [t ln (t) - t]_{x}^{2}

Berechne die Grenzen:

2 ln (2) - 2 - \frac{1}{2} x ln (x) + x

= 2 ln (2) - 2 - \frac{1}{2} x ln (x) + x

Vereinfache

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

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