integral from 3 to 7 of 1/(2x-5)

Lösung

\int_{3}^{7} \frac{1}{2 x - 5} d x

ln (3)

Dezimale

1.09861 \dots

Schritte zur Lösung

\int_{3}^{7} \frac{1}{2 x - 5} d x

Wende U-Substitution an

= \int_{1}^{9} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{1}^{9} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{1}^{9}

Berechne die Grenzen:

2 ln (3)

= \frac{1}{2} \cdot 2 ln (3)

Vereinfache

= ln (3)

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

\int_{- 11}^{- 3} \frac{1}{x} d x

\int_{1}^{e} x^{2} ln^{2} (x) d x

\int_{- 1.25}^{0} (5 x^{3} - 3 x + 6) d x

\int_{0}^{1} x cos (\frac{nπ}{2} x) d x