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

Lösung

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

\frac{4}{5}

Dezimale

0.8

Schritte zur Lösung

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

Wende U-Substitution an

= \int_{16}^{36} \frac{1}{5 u} d u

Entferne die Konstante:

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

= \frac{1}{5} \cdot \int_{16}^{36} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{5} [2 u^{\frac{1}{2}}]_{16}^{36}

Wende Radikal Regel an:

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

= \frac{1}{5} [2 u]_{16}^{36}

Berechne die Grenzen:

4

= \frac{1}{5} \cdot 4

Vereinfache

= \frac{4}{5}

\int_{2}^{5} x^{\frac{1}{3}} (- 1 - 2 x) d x

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