de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^2-12)/(x^3+4x)

Lösung

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

Lösung

2 ln x^{2} + 4 - 3 ln ∣ x ∣ + C

Schritte zur Lösung

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

Multipliziere aus

\frac{x ^{2} - 12}{x ^{3} + 4 x} : \frac{x ^{2}}{x ^{3} + 4 x} - \frac{12}{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{x ^{2}}{x ^{3} + 4 x} d x - \int \frac{12}{x ^{3} + 4 x} d x

\int \frac{x ^{2}}{x ^{3} + 4 x} d x = \frac{1}{2} ln x^{2} + 4

\int \frac{12}{x ^{3} + 4 x} d x = 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4)

= \frac{1}{2} ln x^{2} + 4 - 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4)

Vereinfache

\frac{1}{2} ln x^{2} + 4 - 12 (\frac{1}{4} ln ∣ x ∣ - \frac{1}{8} ln x^{2} + 4) : 2 ln x^{2} + 4 - 3 ln ∣ x ∣

= 2 ln x^{2} + 4 - 3 ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= 2 ln x^{2} + 4 - 3 ln ∣ x ∣ + C

Graph

Beliebte Beispiele

(\partial)/(\partial x)((2xy+3)e^{-xy})

\frac{\partial}{\partial x} ((2 x y + 3) e^{- x y})

derivative of ((x^2-2e^x)/(x+3e^x))

\frac{d}{d x} (\frac{( x ^{2} - 2 e ^{x} )}{x + 3 e ^{x}})

integral of 1/(xsqrt(3x))

\int \frac{1}{x 3 x} d x

derivative of 2ln(x^2+y^2)

\frac{d}{d x} (2 ln (x^{2} + y^{2}))

ty^'=(1-y^2)^{1/2}

t y^{^{'}} = (1 - y^{2})^{\frac{1}{2}}