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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of 14sin(x)

\int 14 sin (x) d x

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

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

integral of \sqrt[3]{2x-4}

\int 3 2 x - 4 d x

integral of (e^{7x})/(e^{7x)+2}

\int \frac{e ^{7 x}}{e ^{7 x} + 2} d x

integral of 1/(\sqrt[3]{x-2)}

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