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Beliebt Rechnen >

integral of (x^4)/(25+4x^2)

Lösung

\int \frac{x ^{4}}{25 + 4 x ^{2}} d x

Lösung

\frac{x ^{3}}{12} - \frac{25}{16} x + \frac{125}{32} arctan (\frac{2}{5} x) + C

Schritte zur Lösung

\int \frac{x ^{4}}{25 + 4 x ^{2}} d x

Lange Division

\frac{x ^{4}}{25 + 4 x ^{2}} : \frac{x ^{2}}{4} - \frac{25}{16} + \frac{625}{16 ( 4 x ^{2} + 25 )}

= \int \frac{x ^{2}}{4} - \frac{25}{16} + \frac{625}{16 ( 4 x ^{2} + 25 )} 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 \frac{x ^{2}}{4} d x - \int \frac{25}{16} d x + \int \frac{625}{16 ( 4 x ^{2} + 25 )} d x

\int \frac{x ^{2}}{4} d x = \frac{x ^{3}}{12}

\int \frac{25}{16} d x = \frac{25}{16} x

\int \frac{625}{16 ( 4 x ^{2} + 25 )} d x = \frac{125}{32} arctan (\frac{2}{5} x)

= \frac{x ^{3}}{12} - \frac{25}{16} x + \frac{125}{32} arctan (\frac{2}{5} x)

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{12} - \frac{25}{16} x + \frac{125}{32} arctan (\frac{2}{5} x) + C

Graph

Beliebte Beispiele

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

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

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

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

integral of e^x(3+3e^x)^4

\int e^{x} (3 + 3 e^{x})^{4} d x

integral of (5-4x)/(sqrt(x^2-3x+2))

\int \frac{5 - 4 x}{x ^{2} - 3 x + 2} d x

integral of (4x)/(5(6x^2-7)^{2/3)}

\int \frac{4 x}{5 ( 6 x ^{2} - 7 ) ^{\frac{2}{3}}} d x