integral of (3-2x)/(5x^2+7)

Lösung

\int \frac{3 - 2 x}{5 x ^{2} + 7} d x

\frac{3}{35} arctan (\frac{5}{7} x) - \frac{1}{5} ln 5 x^{2} + 7 + C

Schritte zur Lösung

\int \frac{3 - 2 x}{5 x ^{2} + 7} d x

Multipliziere aus

\frac{3 - 2 x}{5 x ^{2} + 7} : \frac{3}{5 x ^{2} + 7} - \frac{2 x}{5 x ^{2} + 7}

Wende die Summenregel an:

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

= \int \frac{3}{5 x ^{2} + 7} d x - \int \frac{2 x}{5 x ^{2} + 7} d x

\int \frac{3}{5 x ^{2} + 7} d x = \frac{3}{35} arctan (\frac{5}{7} x)

\int \frac{2 x}{5 x ^{2} + 7} d x = \frac{1}{5} ln 5 x^{2} + 7

= \frac{3}{35} arctan (\frac{5}{7} x) - \frac{1}{5} ln 5 x^{2} + 7

Füge eine Konstante zur Lösung hinzu

= \frac{3}{35} arctan (\frac{5}{7} x) - \frac{1}{5} ln 5 x^{2} + 7 + C