integral from 2 to 5 of x^2ln(x)

Lösung

\int_{2}^{5} x^{2} ln (x) d x

- 13 + \frac{125 ln ( 5 ) - 8 ln ( 2 )}{3}

Dezimale

52.21152 \dots

Schritte zur Lösung

\int_{2}^{5} x^{2} ln (x) d x

Wende die partielle Integration an

= [\frac{1}{3} x^{3} ln (x) - \int \frac{x ^{2}}{3} d x]_{2}^{5}

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

= [\frac{1}{3} x^{3} ln (x) - \frac{x ^{3}}{9}]_{2}^{5}

Berechne die Grenzen:

- 13 + \frac{125 ln ( 5 ) - 8 ln ( 2 )}{3}

= - 13 + \frac{125 ln ( 5 ) - 8 ln ( 2 )}{3}

\int_{0}^{\frac{π}{2}} cos (d) x d x

\int_{1}^{5} x^{\frac{2}{3}} d x

\int_{- 2}^{2} x^{6} sin (x) d x

\int_{0}^{2} 2 x (x + 1) d x

\int_{0}^{2} 5 x^{3} d x