integral from 1 to 4 of (18(ln(x))^5)/x

Lösung

\int_{1}^{4} \frac{18 ( ln ( x ) ) ^{5}}{x} d x

192 ln^{6} (2)

Dezimale

21.29384 \dots

Schritte zur Lösung

\int_{1}^{4} \frac{18 ( ln ( x ) ) ^{5}}{x} d x

Entferne die Konstante:

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

= 18 \cdot \int_{1}^{4} \frac{( ln ( x ) ) ^{5}}{x} d x

Wende U-Substitution an

= 18 \cdot \int_{0}^{2 l n (2)} u^{5} d u

Wende die Potenzregel an

= 18 [\frac{u ^{6}}{6}]_{0}^{2 l n (2)}

Berechne die Grenzen:

\frac{32 ln ^{6} ( 2 )}{3}

= 18 \cdot \frac{32 ln ^{6} ( 2 )}{3}

Vereinfache

= 192 ln^{6} (2)

\int_{0}^{1} \frac{x}{x + 3} d x

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

\int_{- y}^{y} c (y^{2} - x^{2}) e^{- y} d x

\int_{0}^{\frac{5}{11}} \frac{1}{121 x ^{2} + 25} d x

\int_{- 4}^{4} (16 - x^{2} + 2) d x