integral from 0 to 1/3 of xln(3x)

Lösung

\int_{0}^{\frac{1}{3}} x ln (3 x) d x

- \frac{1}{36}

Dezimale

- 0.02777 \dots

Schritte zur Lösung

\int_{0}^{\frac{1}{3}} x ln (3 x) d x

Wende die partielle Integration an

= [\frac{1}{2} (x^{2} ln (3 x) - 2 \cdot \int \frac{x}{2} d x)]_{0}^{\frac{1}{3}}

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

= [\frac{1}{2} (x^{2} ln (3 x) - 2 \cdot \frac{x ^{2}}{4})]_{0}^{\frac{1}{3}}

2 \cdot \frac{x ^{2}}{4} = \frac{x ^{2}}{2}

= [\frac{1}{2} (x^{2} ln (3 x) - \frac{x ^{2}}{2})]_{0}^{\frac{1}{3}}

Berechne die Grenzen:

- \frac{1}{36}

= - \frac{1}{36}

\int_{2}^{5} \frac{1}{( x - 2 ) ^{4}} d x

\int_{0}^{\frac{π}{2}} x cos (7 x) d x

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

\int_{x}^{x^{4}} \frac{y}{x} d y

\int_{0}^{π} sin^{4} (x) cos (x) d x