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

Lösung

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

\frac{1}{2} (ln (11) - ln (3))

Dezimale

0.64964 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{3}^{11} \frac{1}{2 u} d u

Entferne die Konstante:

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

= \frac{1}{2} \cdot \int_{3}^{11} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{3}^{11}

Berechne die Grenzen:

ln (11) - ln (3)

= \frac{1}{2} (ln (11) - ln (3))

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

a re a ∣ x - 2 ∣, 0 = x - 3 y + 6

\int_{2}^{3} \frac{40}{3 - x} d x

\frac{d}{d x} (\frac{cos ( x )}{1 + a sin ( x )})

\int \frac{6}{1 + x ^{2}} d x