integral from 0 to 3 of 1/(sqrt(5x+2))

Lösung

\int_{0}^{3} \frac{1}{5 x + 2} d x

\frac{2 17 - 2 2}{5}

Dezimale

1.08355 \dots

Schritte zur Lösung

\int_{0}^{3} \frac{1}{5 x + 2} d x

Wende U-Substitution an

= \int_{2}^{17} \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_{2}^{17} \frac{1}{u} d u

Wende die Potenzregel an

= \frac{1}{5} [2 u^{\frac{1}{2}}]_{2}^{17}

Wende Radikal Regel an:

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

= \frac{1}{5} [2 u]_{2}^{17}

Berechne die Grenzen:

217 - 22

= \frac{1}{5} (217 - 22)

Vereinfache

= \frac{2 17 - 2 2}{5}

\int_{1}^{\infty} x^{- \frac{1}{p}} d x

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