integral from 2 to 4 of 4/(x(ln(x))^2)

Lösung

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

\frac{2}{ln ( 2 )}

Dezimale

2.88539 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 4 \cdot \int_{2}^{4} \frac{1}{x ( ln ( x ) ) ^{2}} d x

Wende U-Substitution an

= 4 \cdot \int_{l n (2)}^{2 l n (2)} \frac{1}{u ^{2}} d u

Wende die Potenzregel an

= 4 [- \frac{1}{u}]_{l n (2)}^{2 l n (2)}

Berechne die Grenzen:

\frac{1}{2 ln ( 2 )}

= 4 \cdot \frac{1}{2 ln ( 2 )}

Vereinfache

= \frac{2}{ln ( 2 )}

\int_{0}^{l n (9)} e^{x - e^{x}} d x

\int_{0}^{2} - x + 1 d x

\int_{- 4}^{4} x^{2} + x - 2 d x

\int_{0}^{1} π (1 - x) d x

\int_{x^{3}}^{x} y d y