integral from 1 to 2 of 4/(2x+3)

Lösung

\int_{1}^{2} \frac{4}{2 x + 3} d x

2 (ln (7) - ln (5))

Dezimale

0.67294 \dots

Schritte zur Lösung

\int_{1}^{2} \frac{4}{2 x + 3} d x

Entferne die Konstante:

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

= 4 \cdot \int_{1}^{2} \frac{1}{2 x + 3} d x

Wende U-Substitution an

= 4 \cdot \int_{5}^{7} \frac{1}{2 u} d u

Entferne die Konstante:

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

= 4 \cdot \frac{1}{2} \cdot \int_{5}^{7} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 \cdot \frac{1}{2} [ln ∣ u ∣]_{5}^{7}

Vereinfache

4 \cdot \frac{1}{2} [ln ∣ u ∣]_{5}^{7} : 2 [ln ∣ u ∣]_{5}^{7}

= 2 [ln ∣ u ∣]_{5}^{7}

Berechne die Grenzen:

ln (7) - ln (5)

= 2 (ln (7) - ln (5))

l a pl a ce t r an s f or m 2 (t - 2)

\int \frac{1}{16 x ^{2} - 24 x - 27} d x

d er i v a t i v e \frac{x}{5}

d er i v a t i v e y = 7 cos (x)

\int t^{2} \cdot ln^{2} (t) d t