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

Lösung

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

\frac{2}{3} ln (\frac{7}{4})

Dezimale

0.37307 \dots

Schritte zur Lösung

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

Entferne die Konstante:

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

= 2 \cdot \int_{1}^{3} \frac{1}{5 + 3 x} d x

Wende U-Substitution an

= 2 \cdot \int_{8}^{14} \frac{1}{3 u} d u

Entferne die Konstante:

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

= 2 \cdot \frac{1}{3} \cdot \int_{8}^{14} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 \cdot \frac{1}{3} [ln ∣ u ∣]_{8}^{14}

Vereinfache

2 \cdot \frac{1}{3} [ln ∣ u ∣]_{8}^{14} : \frac{2}{3} [ln ∣ u ∣]_{8}^{14}

= \frac{2}{3} [ln ∣ u ∣]_{8}^{14}

Berechne die Grenzen:

ln (14) - 3 ln (2)

= \frac{2}{3} (ln (14) - 3 ln (2))

Vereinfache

= \frac{2}{3} ln (\frac{7}{4})

\int_{- 1}^{1} e^{- \frac{x ^{2}}{2}} d x

\int_{0}^{4} (3 - 3 x) d x

\int_{0}^{1} sin (π x^{2}) x d x

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

\int_{0}^{\frac{π}{2}} \frac{1}{2}