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Beliebt Rechnen >

integral from 1 to 5 of 1/(1+sqrt(x-1))

Lösung

\int_{1}^{5} \frac{1}{1 + x - 1} d x

Lösung

2 (2 - ln (3))

+1

Dezimale

1.80277 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{1}{1 + x - 1} d x

Wende U-Substitution an

= \int_{0}^{2} \frac{2 u}{1 + u} d u

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int_{0}^{2} \frac{u}{1 + u} d u

Wende U-Substitution an

= 2 \cdot \int_{1}^{3} \frac{v - 1}{v} d v

Multipliziere aus

\frac{v - 1}{v} : 1 - \frac{1}{v}

= 2 \cdot \int_{1}^{3} 1 - \frac{1}{v} d v

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 2 (\int_{1}^{3} 1 d v - \int_{1}^{3} \frac{1}{v} d v)

\int_{1}^{3} 1 d v = 2

\int_{1}^{3} \frac{1}{v} d v = ln (3)

= 2 (2 - ln (3))

Graph

Beliebte Beispiele

integral from-2 to 2 of 1-x^2

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

integral from 0 to ln(2) of (e^t-e^{-t})

\int_{0}^{l n (2)} (e^{t} - e^{- t}) d t

integral from 1 to 6 of 7x+1

\int_{1}^{6} 7 x + 1 d x

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

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

integral from-2 to 2 of y^2

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