integral from 1 to e^3 of (4ln(x))/x

Lösung

\int_{1}^{e^{3}} \frac{4 ln ( x )}{x} d x

18

Schritte zur Lösung

\int_{1}^{e^{3}} \frac{4 ln ( x )}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{e^{3}} \frac{ln ( x )}{x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{3} u d u

Wende die Potenzregel an

= 4 [\frac{u ^{2}}{2}]_{0}^{3}

Berechne die Grenzen:

\frac{9}{2}

= 4 \cdot \frac{9}{2}

Vereinfache

= 18

\int_{- 1}^{3} 3 x^{2} + 8 x d x

\int_{6}^{7} 3^{x} d x

\int_{1}^{\infty} arccot (x) d x

\int_{0}^{\frac{3 π}{2}} 7 sin (x) d x

\int_{0}^{1} x^{3} e^{- 4 x} d x