integral from 1 to 4 of x^{1/2}ln(x)

Lösung

\int_{1}^{4} x^{\frac{1}{2}} ln (x) d x

- \frac{28}{9} + \frac{32}{3} ln (2)

Dezimale

4.28245 \dots

Schritte zur Lösung

\int_{1}^{4} x^{\frac{1}{2}} ln (x) d x

Wende die partielle Integration an

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \int \frac{2}{3} x^{\frac{1}{2}} d x]_{1}^{4}

\int \frac{2}{3} x^{\frac{1}{2}} d x = \frac{4}{9} x^{\frac{3}{2}}

= [\frac{2}{3} x^{\frac{3}{2}} ln (x) - \frac{4}{9} x^{\frac{3}{2}}]_{1}^{4}

Berechne die Grenzen:

- \frac{28}{9} + \frac{32}{3} ln (2)

= - \frac{28}{9} + \frac{32}{3} ln (2)

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