integral of (4x-2)/(x^4+x^2)

Lösung

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

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

Schritte zur Lösung

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

Multipliziere aus

\frac{4 x - 2}{x ^{4} + x ^{2}} : \frac{4 x}{x ^{4} + x ^{2}} - \frac{2}{x ^{4} + x ^{2}}

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

d er i v a t i v e y = ln (x^{2} - 4)

x \to 2 lim (3 - x^{\frac{1}{x ^{2}}})

\frac{d}{d x} ((x) d x)

\frac{d}{d x} (cos (\frac{1 - e ^{6 x}}{1 + e ^{6 x}}))

x \to \infty lim (9.9)