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Beliebt Rechnen >

integral of (4x^5-4)/(x^2-4)

Lösung

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

Lösung

x^{4} + 8 x^{2} + 33 ln ∣ x + 2 ∣ + 31 ln ∣ x - 2 ∣ + C

Schritte zur Lösung

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

Lange Division

\frac{4 x ^{5} - 4}{x ^{2} - 4} : 4 x^{3} + 16 x + \frac{64 x - 4}{x ^{2} - 4}

= \int 4 x^{3} + 16 x + \frac{64 x - 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 4 x^{3} d x + \int 16 x d x + \int \frac{64 x - 4}{x ^{2} - 4} d x

\int 4 x^{3} d x = x^{4}

\int 16 x d x = 8 x^{2}

\int \frac{64 x - 4}{x ^{2} - 4} d x = 33 ln ∣ x + 2 ∣ + 31 ln ∣ x - 2 ∣

= x^{4} + 8 x^{2} + 33 ln ∣ x + 2 ∣ + 31 ln ∣ x - 2 ∣

Füge eine Konstante zur Lösung hinzu

= x^{4} + 8 x^{2} + 33 ln ∣ x + 2 ∣ + 31 ln ∣ x - 2 ∣ + C

Graph

Beliebte Beispiele

sum from n=1 to infinity of n/(1+n^2)

n = 1 \sum \infty \frac{n}{1 + n ^{2}}

(\partial)/(\partial y)(ln(e^x+e^y))

\frac{\partial}{\partial y} (ln (e^{x} + e^{y}))

derivative arccos(1-x^2)

d er i v a t i v e arccos (1 - x^{2})

derivative of ((x-1)/2)

\frac{d}{d x} (\frac{( x - 1 )}{2})

integral of 1/(7-4x-x^2)

\int \frac{1}{7 - 4 x - x ^{2}} d x