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

Lösung

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

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

Dezimale

0.45814 \dots

Schritte zur Lösung

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

Wende U-Substitution an

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

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{2}^{5}

Berechne die Grenzen:

ln (5) - ln (2)

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

\int_{0}^{1} 2 t d t

\int_{0}^{\frac{π}{3}} sin^{6} (x) d x

\int_{- 1}^{2} t sin (t^{2}) + 2 t^{3} d t

\int_{- 2}^{5} - \frac{5}{x ^{2}} d x

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