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Beliebt Rechnen >

integral from 1 to 5 of 1/(sqrt(3x+1))

Lösung

\int_{1}^{5} \frac{1}{3 x + 1} d x

Lösung

\frac{4}{3}

+1

Dezimale

1.33333 \dots

Schritte zur Lösung

\int_{1}^{5} \frac{1}{3 x + 1} d x

Wende U-Substitution an

= \int_{4}^{16} \frac{1}{3 u} d u

Entferne die Konstante:

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

= \frac{1}{3} \cdot \int_{4}^{16} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{3} [2 u^{\frac{1}{2}}]_{4}^{16}

Wende Radikal Regel an:

a^{\frac{1}{n}} = n a

= \frac{1}{3} [2 u]_{4}^{16}

Berechne die Grenzen:

4

= \frac{1}{3} \cdot 4

Vereinfache

= \frac{4}{3}

Graph

Beliebte Beispiele

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\int_{1}^{e} ln (2 x) d x

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