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Beliebt Rechnen >

integral of 1/(2*x^2-x-3)

Lösung

\int \frac{1}{2 \cdot x ^{2} - x - 3} d x

Lösung

- \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣ + C

Schritte zur Lösung

\int \frac{1}{2 x ^{2} - x - 3} d x

Ermittle den Partialbruch von

\frac{1}{2 x ^{2} - x - 3} : - \frac{1}{5 ( x + 1 )} + \frac{2}{5 ( 2 x - 3 )}

= \int - \frac{1}{5 ( x + 1 )} + \frac{2}{5 ( 2 x - 3 )} 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{1}{5 ( x + 1 )} d x + \int \frac{2}{5 ( 2 x - 3 )} d x

\int \frac{1}{5 ( x + 1 )} d x = \frac{1}{5} ln ∣ x + 1 ∣

\int \frac{2}{5 ( 2 x - 3 )} d x = \frac{1}{5} ln ∣ 2 x - 3 ∣

= - \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{5} ln ∣ x + 1 ∣ + \frac{1}{5} ln ∣ 2 x - 3 ∣ + C

Graph

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(\partial)/(\partial s)(e^{st})

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\int (2 sin (x) - 3 cos (x) + \frac{1}{2}) d x

integral of csc^2(t)

\int csc^{2} (t) d t

inverselaplace 2/((s+3)^2-9)

in v erse l a pl a ce \frac{2}{( s + 3 ) ^{2} - 9}

integral of csc^2(5y)

\int csc^{2} (5 y) d y