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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{1}{2} ln (31)

+1

Dezimale

1.71699 \dots

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{2}^{62} \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}^{62} \frac{1}{u} d u

Nutze das gemeinsame Integral :

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{1}{2} [ln ∣ u ∣]_{2}^{62}

Berechne die Grenzen:

ln (62) - ln (2)

= \frac{1}{2} (ln (62) - ln (2))

Vereinfache

= \frac{1}{2} ln (31)

Graph

Beliebte Beispiele

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\int 2 tan^{4} (x se) c^{6} x d x

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