integral from 0 to 1 of 2/(3+x)

Lösung

\int_{0}^{1} \frac{2}{3 + x} d x

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

Dezimale

0.57536 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{2}{3 + x} d x

Entferne die Konstante:

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

= 2 \cdot \int_{0}^{1} \frac{1}{3 + x} d x

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 [ln ∣ u ∣]_{3}^{4}

Berechne die Grenzen:

2 ln (2) - ln (3)

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

\int_{8}^{27} (3 x - \frac{1}{3 x}) d x

\int_{- 2}^{- 1} \frac{1}{( x - 1 ) ^{2}} d x

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

\int_{0}^{1} x x + 3 d x

\int_{0}^{4} \frac{3}{16} x d x