integral of ((x^2)/3-3/(2x-3)-e^{3x})

Lösung

\int (\frac{x ^{2}}{3} - \frac{3}{2 x - 3} - e^{3 x}) d x

\frac{x ^{3}}{9} - \frac{3}{2} ln ∣ 2 x - 3 ∣ - \frac{1}{3} e^{3 x} + C

Schritte zur Lösung

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

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

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

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

\int e^{3 x} d x = \frac{1}{3} e^{3 x}

= \frac{x ^{3}}{9} - \frac{3}{2} ln ∣ 2 x - 3 ∣ - \frac{1}{3} e^{3 x}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{9} - \frac{3}{2} ln ∣ 2 x - 3 ∣ - \frac{1}{3} e^{3 x} + C

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in t e g r a l \frac{2 x}{9 x ^{2} - 6 x - 8}

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