integral from 0 to s of 1/(0.2s+10)

Lösung

\int_{0}^{s} \frac{1}{0.2 s + 10} d s

5 (ln ∣ 0.2 s + 10 ∣ - 2.30258 \dots)

Schritte zur Lösung

\int_{0}^{s} \frac{1}{0.2 s + 10} d s

Wende U-Substitution an

= \int_{10}^{0.2 s + 10} \frac{1}{0.2 u} d u

Entferne die Konstante:

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

= \frac{1}{0.2} \cdot \int_{10}^{0.2 s + 10} \frac{1}{u} d u

Vereinfache

= 5 \cdot \int_{10}^{0.2 s + 10} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= 5 [ln ∣ u ∣]_{10}^{0.2 s + 10}

Berechne die Grenzen:

ln ∣ 0.2 s + 10 ∣ - 2.30258 \dots

= 5 (ln ∣ 0.2 s + 10 ∣ - 2.30258 \dots)

\frac{\partial}{\partial x} (3 x^{2} - 4 x y + x yz)

y^{^{'}} = x^{2} - 2

\int \frac{4 x}{x - 1} d x

y^{^{'}} = 5 t y^{2}

d er i v a t i v e 9 x^{- 2}