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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Lange Division

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

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

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

\int 1 d x = x

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

= \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 sec(x)tan(x)cos(sec(x))

\int sec (x) tan (x) cos (sec (x)) d x

integral of 9xsqrt(6x-3)

\int 9 x 6 x - 3 d x

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

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

integral of 8xsqrt(x^2+1)

\int 8 x x^{2} + 1 d x

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

\int \frac{1}{3 x + 1 + 1} d x