integral from 0 to 1 of 3/(2x-5)

Lösung

\int_{0}^{1} \frac{3}{2 x - 5} d x

\frac{3}{2} (ln (3) - ln (5))

Dezimale

- 0.76623 \dots

Schritte zur Lösung

\int_{0}^{1} \frac{3}{2 x - 5} d x

Entferne die Konstante:

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

= 3 \cdot \int_{0}^{1} \frac{1}{2 x - 5} d x

Wende U-Substitution an

= 3 \cdot \int_{- 5}^{- 3} \frac{1}{2 u} d u

Entferne die Konstante:

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

= 3 \cdot \frac{1}{2} \cdot \int_{- 5}^{- 3} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 \cdot \frac{1}{2} [ln ∣ u ∣]_{- 5}^{- 3}

Vereinfache

3 \cdot \frac{1}{2} [ln ∣ u ∣]_{- 5}^{- 3} : \frac{3}{2} [ln ∣ u ∣]_{- 5}^{- 3}

= \frac{3}{2} [ln ∣ u ∣]_{- 5}^{- 3}

Berechne die Grenzen:

ln (3) - ln (5)

= \frac{3}{2} (ln (3) - ln (5))

\int_{0}^{1} 19 \frac{1}{x ^{p}} d x

in v erse l a pl a ce \frac{3}{s ( 6 s ^{2} + 5 s + 1 )}

\frac{\partial}{\partial y} (cos (x yz))

y^{^{''}} + 45 y^{^{'}} + 20 y = 0, y (0) = 1, y^{^{'}} (0) = 0

n = 1 \sum \infty n e^{3 n}