integral from 1 to 7 of (4(ln(x))^3)/x

Lösung

\int_{1}^{7} \frac{4 ( ln ( x ) ) ^{3}}{x} d x

ln^{4} (7)

Dezimale

14.33808 \dots

Schritte zur Lösung

\int_{1}^{7} \frac{4 ( ln ( x ) ) ^{3}}{x} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{7} \frac{( ln ( x ) ) ^{3}}{x} d x

Wende U-Substitution an

= 4 \cdot \int_{0}^{l n (7)} u^{3} d u

Wende die Potenzregel an

= 4 [\frac{u ^{4}}{4}]_{0}^{l n (7)}

Berechne die Grenzen:

\frac{ln ^{4} ( 7 )}{4}

= 4 \cdot \frac{ln ^{4} ( 7 )}{4}

Vereinfache

= ln^{4} (7)

\int_{0}^{3} \frac{x}{x ^{2} - 7 x + 12} d x

\int_{2}^{4} 8 x^{2} d x

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

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

\int_{- π}^{0} 2 x sin (n x) d x