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Beliebt Rechnen >

integral of (6x^2+8)/(x^3+4x)

Lösung

\int \frac{6 x ^{2} + 8}{x ^{3} + 4 x} d x

Lösung

2 ln x^{2} + 4 + 2 ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{6 x ^{2} + 8}{x ^{3} + 4 x} d x

Multipliziere aus

\frac{6 x ^{2} + 8}{x ^{3} + 4 x} : \frac{6 x ^{2}}{x ^{3} + 4 x} + \frac{8}{x ^{3} + 4 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{6 x ^{2}}{x ^{3} + 4 x} d x + \int \frac{8}{x ^{3} + 4 x} d x

\int \frac{6 x ^{2}}{x ^{3} + 4 x} d x = 3 ln x^{2} + 4

\int \frac{8}{x ^{3} + 4 x} d x = 2 ln ∣ x ∣ - ln x^{2} + 4

= 3 ln x^{2} + 4 + 2 ln ∣ x ∣ - ln x^{2} + 4

Vereinfache

= 2 ln x^{2} + 4 + 2 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln x^{2} + 4 + 2 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

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\frac{d y}{d x} + y = e^{7 x}

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y^{^{'}} - \frac{5}{x} y = \frac{y ^{5}}{x ^{18}}

integral from 9 to 16 of 1/(7-sqrt(x))

\int_{9}^{16} \frac{1}{7 - x} d x

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\int \frac{x}{x - 16} d x

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n = 0 \sum \infty n^{2} (x)^{n - 1}