integral of (5000q)/(25q+1500)

Lösung

\int \frac{5000 q}{25 q + 1500} d q

5000 (\frac{1}{25} q - \frac{12}{5} ln ∣ q + 60 ∣) + C

Schritte zur Lösung

\int \frac{5000 q}{25 q + 1500} d q

Entferne die Konstante:

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

= 5000 \cdot \int \frac{q}{25 q + 1500} d q

Lange Division

\frac{q}{25 q + 1500} : \frac{1}{25} - \frac{12}{5 ( q + 60 )}

= 5000 \cdot \int \frac{1}{25} - \frac{12}{5 ( q + 60 )} d q

Wende die Summenregel an:

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

= 5000 (\int \frac{1}{25} d q - \int \frac{12}{5 ( q + 60 )} d q)

\int \frac{1}{25} d q = \frac{1}{25} q

\int \frac{12}{5 ( q + 60 )} d q = \frac{12}{5} ln ∣ q + 60 ∣

= 5000 (\frac{1}{25} q - \frac{12}{5} ln ∣ q + 60 ∣)

Füge eine Konstante zur Lösung hinzu

= 5000 (\frac{1}{25} q - \frac{12}{5} ln ∣ q + 60 ∣) + C

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