integral from 2 to 7 of x/(x^2+1)

Lösung

\int_{2}^{7} \frac{x}{x ^{2} + 1} d x

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

Dezimale

1.15129 \dots

Schritte zur Lösung

\int_{2}^{7} \frac{x}{x ^{2} + 1} d x

Wende U-Substitution an

= \int_{5}^{50} \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_{5}^{50} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{5}^{50}

Berechne die Grenzen:

ln (50) - ln (5)

= \frac{1}{2} (ln (50) - ln (5))

Vereinfache

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

\int_{- 1}^{1} 2 y d y

\int_{0}^{8} \frac{2}{( x + 2 ) ^{2}} d x

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

\int_{2}^{3} 6 x^{2} d x

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