integral of (3-10x)/(4x^2+9)

Lösung

\int \frac{3 - 10 x}{4 x ^{2} + 9} d x

\frac{1}{2} arctan (\frac{2}{3} x) - \frac{5}{4} ln 4 x^{2} + 9 + C

Schritte zur Lösung

\int \frac{3 - 10 x}{4 x ^{2} + 9} d x

Multipliziere aus

\frac{3 - 10 x}{4 x ^{2} + 9} : \frac{3}{4 x ^{2} + 9} - \frac{10 x}{4 x ^{2} + 9}

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}{4 x ^{2} + 9} d x - \int \frac{10 x}{4 x ^{2} + 9} d x

\int \frac{3}{4 x ^{2} + 9} d x = \frac{1}{2} arctan (\frac{2}{3} x)

\int \frac{10 x}{4 x ^{2} + 9} d x = \frac{5}{4} ln 4 x^{2} + 9

= \frac{1}{2} arctan (\frac{2}{3} x) - \frac{5}{4} ln 4 x^{2} + 9

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} arctan (\frac{2}{3} x) - \frac{5}{4} ln 4 x^{2} + 9 + C

\int \frac{3}{x ^{2} - 9} d x

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