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Beliebt Rechnen >

integral of (sqrt(2x^2-4))/(x^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

y^{''}-5y^'+4y=0,y(0)=-1/2 ,y^'(0)=-17/4

y^{^{''}} - 5 y^{^{'}} + 4 y = 0, y (0) = - \frac{1}{2}, y^{^{'}} (0) = - \frac{17}{4}

derivative of x^{3/2}+4

\frac{d}{d x} (x^{\frac{3}{2}} + 4)

y^{'''}-y^{''}-y^'+y=0

y^{^{'''}} - y^{^{''}} - y^{^{'}} + y = 0

derivative of (1+e^{-x}^{sqrt(x)})

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

integral of 3x^3e^{3x}

\int 3 x^{3} e^{3 x} d x