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Beliebt Rechnen >

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

Lösung

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

Lösung

- \frac{1}{4 x} - \frac{1}{8} arctan (\frac{x}{2}) + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

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

\int \frac{1}{4 ( x ^{2} + 4 )} d x = \frac{1}{8} arctan (\frac{x}{2})

= - \frac{1}{4 x} - \frac{1}{8} arctan (\frac{x}{2})

Füge eine Konstante zur Lösung hinzu

= - \frac{1}{4 x} - \frac{1}{8} arctan (\frac{x}{2}) + C

Graph

Beliebte Beispiele

integral of 1/((2-3x)^2)

\int \frac{1}{( 2 - 3 x ) ^{2}} d x

integral of sec(2x+4)tan(2x+4)

\int sec (2 x + 4) tan (2 x + 4) d x

integral of (ln(x+1)-ln(x))/(x(x+1))

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

integral of (x^5-1)/(x^4-1)

\int \frac{x ^{5} - 1}{x ^{4} - 1} d x

integral of (sqrt(x)-x)^2

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