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

Lösung

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

\frac{1}{2} ln (5)

Dezimale

0.80471 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{10} \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_{2}^{10} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{2}^{10}

Berechne die Grenzen:

ln (10) - ln (2)

= \frac{1}{2} (ln (10) - ln (2))

Vereinfache

= \frac{1}{2} ln (5)

d er i v a t i v e 2 - lo g_{10} (a)

\int \frac{12 x ^{2}}{2 x + 1} d x

x \to 0 lim (\frac{4 x ^{2} - 2 x}{x})

\frac{\partial}{\partial x} (ln (x^{2} + 3 y^{2} + 8))

\int \frac{1}{( x - 2 ) ( x - 4 ) ( x + 1 )} d x