integral from 2 to 4 of 3xln(x)

Lösung

\int_{2}^{4} 3 x ln (x) d x

3 (14 ln (2) - 3)

Dezimale

20.11218 \dots

Schritte zur Lösung

\int_{2}^{4} 3 x ln (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{2}^{4} x ln (x) d x

Wende die partielle Integration an

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

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

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

Berechne die Grenzen:

14 ln (2) - 3

= 3 (14 ln (2) - 3)

\int_{y}^{8 - y^{2}} 1 d x

\int_{2}^{3} \frac{x}{8} d x

\int_{0}^{1} x^{4} + 1 d x

\int_{0}^{5} 11 + x^{2} d x

\int_{1}^{4} \frac{1}{2 t} d t