integral from 0 to 5 of 1/(sqrt(7x+3))

Lösung

\int_{0}^{5} \frac{1}{7 x + 3} d x

\frac{2 38 - 2 3}{7}

Dezimale

1.26638 \dots

Schritte zur Lösung

\int_{0}^{5} \frac{1}{7 x + 3} d x

Wende U-Substitution an

= \int_{3}^{38} \frac{1}{7 u} d u

Entferne die Konstante:

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

= \frac{1}{7} \cdot \int_{3}^{38} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{7} [2 u^{\frac{1}{2}}]_{3}^{38}

Wende Radikal Regel an:

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

= \frac{1}{7} [2 u]_{3}^{38}

Berechne die Grenzen:

238 - 23

= \frac{1}{7} (238 - 23)

Vereinfache

= \frac{2 38 - 2 3}{7}

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