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Beliebt Rechnen >

integral of (2x-3)/(2x^3+2x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Multipliziere aus

\frac{2 x - 3}{2 x ^{3} + 2 x} : \frac{2 x}{2 x ^{3} + 2 x} - \frac{3}{2 x ^{3} + 2 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{2 x}{2 x ^{3} + 2 x} d x - \int \frac{3}{2 x ^{3} + 2 x} d x

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

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

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

integral of sqrt(x)+1/(x^2)

\int x + \frac{1}{x ^{2}} d x

integral of (tan^2(θ))/(sec^2(θ))

\int \frac{tan ^{2} ( θ )}{sec ^{2} ( θ )} d θ

integral of e^{-3t}cos(2t)

\int e^{- 3 t} cos (2 t) d t

integral of sqrt(a^2-u^2)

\int a^{2} - u^{2} d u