integral of (4x^2-7)/(2x-3)

Lösung

\int \frac{4 x ^{2} - 7}{2 x - 3} d x

x^{2} + 3 x + ln ∣ 2 x - 3 ∣ + C

Schritte zur Lösung

\int \frac{4 x ^{2} - 7}{2 x - 3} d x

Multipliziere aus

\frac{4 x ^{2} - 7}{2 x - 3} : \frac{4 x ^{2}}{2 x - 3} - \frac{7}{2 x - 3}

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

\int \frac{4 x ^{2}}{2 x - 3} d x = x^{2} + 3 x + \frac{9}{2} ln ∣ 2 x - 3 ∣

\int \frac{7}{2 x - 3} d x = \frac{7}{2} ln ∣ 2 x - 3 ∣

= x^{2} + 3 x + \frac{9}{2} ln ∣ 2 x - 3 ∣ - \frac{7}{2} ln ∣ 2 x - 3 ∣

Addiere gleiche Elemente:

\frac{9}{2} ln ∣ 2 x - 3 ∣ - \frac{7}{2} ln ∣ 2 x - 3 ∣ = ln ∣ 2 x - 3 ∣

= x^{2} + 3 x + ln ∣ 2 x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= x^{2} + 3 x + ln ∣ 2 x - 3 ∣ + C

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