integral from 2 to 3 of 7/x+x^{-1}

Lösung

\int_{2}^{3} \frac{7}{x} + x^{- 1} d x

8 (ln (3) - ln (2))

Dezimale

3.24372 \dots

Schritte zur Lösung

\int_{2}^{3} \frac{7}{x} + x^{- 1} d x

Vereinfache

\frac{7}{x} + x^{- 1} : \frac{8}{x}

= \int_{2}^{3} \frac{8}{x} d x

Entferne die Konstante:

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

= 8 \cdot \int_{2}^{3} \frac{1}{x} d x

Nutze das gemeinsame Integral :

\int \frac{1}{x} d x = ln (∣ x ∣)

= 8 [ln ∣ x ∣]_{2}^{3}

Berechne die Grenzen:

ln (3) - ln (2)

= 8 (ln (3) - ln (2))

\int_{- 1}^{0} (2 x + 1)^{4} (x + 1) d x

\int_{- 1}^{2} 4 x + x^{2} d x

\int_{0}^{a} \frac{1}{2 x + 1} d x

\int_{0}^{π} sin (θ) d θ

\int_{1}^{e} (ln (x))^{7} d x