integral of (3x-1)/(x^2-4)

Lösung

\int \frac{3 x - 1}{x ^{2} - 4} d x

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

Schritte zur Lösung

\int \frac{3 x - 1}{x ^{2} - 4} d x

Multipliziere aus

\frac{3 x - 1}{x ^{2} - 4} : \frac{3 x}{x ^{2} - 4} - \frac{1}{x ^{2} - 4}

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 x}{x ^{2} - 4} d x - \int \frac{1}{x ^{2} - 4} d x

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

\int \frac{1}{x ^{2} - 4} d x = - \frac{1}{4} (ln \frac{x}{2} + 1 - ln \frac{x}{2} - 1)

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

l a pl a ce t r an s f or m - 3 (sin (4 (t - \frac{5 π}{4})))

\frac{\partial}{\partial x} (\frac{1}{7 + 5 x})

\int (x^{3} + 2)^{2} (3 x^{2}) d x

\int_{0}^{2} - 4 x^{3} x^{2} + 4 d x

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