integral from 0 to 4 of xln(5-x)

Lösung

\int_{0}^{4} x ln (5 - x) d x

- 14 + \frac{25}{2} ln (5)

Dezimale

6.11797 \dots

Schritte zur Lösung

\int_{0}^{4} x ln (5 - x) d x

Wende die partielle Integration an

= [\frac{1}{2} x^{2} ln (5 - x) - \int - \frac{x ^{2}}{2 ( 5 - x )} d x]_{0}^{4}

\int - \frac{x ^{2}}{2 ( 5 - x )} d x = - \frac{1}{2} (- \frac{x ^{2}}{2} - 5 x - 25 ln ∣ - x + 5 ∣)

= [\frac{1}{2} x^{2} ln (5 - x) - (- \frac{1}{2} (- \frac{x ^{2}}{2} - 5 x - 25 ln ∣ - x + 5 ∣))]_{0}^{4}

Vereinfache

= [\frac{1}{2} x^{2} ln (5 - x) + \frac{1}{2} (- \frac{x ^{2}}{2} - 5 x - 25 ln ∣ - x + 5 ∣)]_{0}^{4}

Berechne die Grenzen:

- 14 + \frac{25}{2} ln (5)

= - 14 + \frac{25}{2} ln (5)

\int_{0}^{5} x e^{5 x} d x

\int_{1}^{5} (2 x + 1) d x

\int_{- 1}^{0} - 20 x e^{- x} d x

\int_{- 3}^{- 1} (- 2 x - 3) d x

\int_{0}^{1} c x^{2} d x