integral from 1 to e of 6/x

Lösung

\int_{1}^{e} \frac{6}{x} d x

6

Schritte zur Lösung

\int_{1}^{e} \frac{6}{x} d x

Entferne die Konstante:

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

= 6 \cdot \int_{1}^{e} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 6 [ln ∣ x ∣]_{1}^{e}

Berechne die Grenzen:

1

= 6 \cdot 1

Vereinfache

= 6

\int_{1}^{\infty} e^{x^{2}} d x

\int_{0}^{3} (3 x^{2} - x^{3}) d x

\int_{0}^{4} 8 x + x d x

\int_{- 1}^{1} - 6 x^{3} - 16 x^{2} + 6 x + 16 d x

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