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Beliebt Rechnen >

integral of 1/(9x^4+x^2)

Lösung

\int \frac{1}{9 x ^{4} + x ^{2}} d x

Lösung

- \frac{1}{x} - 3 arctan (3 x) + C

Schritte zur Lösung

\int \frac{1}{9 x ^{4} + x ^{2}} d x

Ermittle den Partialbruch von

\frac{1}{9 x ^{4} + x ^{2}} : \frac{1}{x ^{2}} - \frac{9}{9 x ^{2} + 1}

= \int \frac{1}{x ^{2}} - \frac{9}{9 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 \frac{1}{x ^{2}} d x - \int \frac{9}{9 x ^{2} + 1} d x

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

\int \frac{9}{9 x ^{2} + 1} d x = 3 arctan (3 x)

= - \frac{1}{x} - 3 arctan (3 x)

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{x} - 3 arctan (3 x) + C

Graph

Beliebte Beispiele

integral of 5/(x^{1/2)}

\int \frac{5}{x ^{\frac{1}{2}}} d x

integral of (3x)/(1+9x^2)

\int \frac{3 x}{1 + 9 x ^{2}} d x

integral of 4/(3x^2)

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

integral of 5csc(x)cot(x)

\int 5 csc (x) cot (x) d x

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

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