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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{x ^{3}}{3} + x + arctan (x) + C

Schritte zur Lösung

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

Multipliziere aus

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

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

\int \frac{x ^{4}}{1 + x ^{2}} d x = \frac{x ^{3}}{3} - x + arctan (x)

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

Vereinfache

= - \frac{x ^{3}}{3} + x + arctan (x)

Füge eine Konstante zur Lösung hinzu

= - \frac{x ^{3}}{3} + x + arctan (x) + C

Graph

Beliebte Beispiele

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

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

integral of e^{2x}csc(e^{2x})

\int e^{2 x} csc (e^{2 x}) d x

integral of sin^5(3x)cos^2(3x)

\int sin^{5} (3 x) cos^{2} (3 x) d x

integral of cos^9(5x)sin(5x)

\int cos^{9} (5 x) sin (5 x) d x

integral of sec^4(1/2 x)

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