integral from-2 to 4 of (|x+1|)/(|x+6|)

Lösung

\int_{- 2}^{4} \frac{∣ x + 1 ∣}{∣ x + 6 ∣} d x

5 ln (5) + 4 - 15 ln (2)

Dezimale

1.64998 \dots

Schritte zur Lösung

\int_{- 2}^{4} \frac{∣ x + 1 ∣}{∣ x + 6 ∣} d x

Entferne die Extremwerte

= \int_{- 2}^{- 1} \frac{- x - 1}{x + 6} d x + \int_{- 1}^{4} \frac{x + 1}{x + 6} d x

\int_{- 2}^{- 1} \frac{- x - 1}{x + 6} d x = - 10 ln (2) + 5 ln (5) - 1

\int_{- 1}^{4} \frac{x + 1}{x + 6} d x = - 5 ln (2) + 5

= - 10 ln (2) + 5 ln (5) - 1 - 5 ln (2) + 5

Vereinfache

= 5 ln (5) + 4 - 15 ln (2)

\int_{0}^{\frac{π}{2}} 15 sin^{7} (x) d x

\int_{0}^{\frac{π}{6}} cos (x) d x

\int_{0}^{1} (\frac{x}{1 + x ^{4}}) d x

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

\int_{1}^{3} \frac{x + 3}{x ^{2} + 6 x} d x