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Beliebt Rechnen >

integral of arctanh(x)

Lösung

\int arctanh (x) d x

Lösung

x arctanh (x) + \frac{1}{2} ln 1 - x^{2} + C

Schritte zur Lösung

\int arctanh (x) d x

Wende die partielle Integration an

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

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

= x arctanh (x) - (- \frac{1}{2} ln 1 - x^{2})

Vereinfache

= x arctanh (x) + \frac{1}{2} ln 1 - x^{2}

Füge eine Konstante zur Lösung hinzu

= x arctanh (x) + \frac{1}{2} ln 1 - x^{2} + C

Graph

Beliebte Beispiele

integral of (x^2)/(e^{3x)}

\int \frac{x ^{2}}{e ^{3 x}} d x

fläche x=7y^2,x=4+6y^2

a re a x = 7 y^{2}, x = 4 + 6 y^{2}

derivative of (-2ln(x+1)/(x^3))

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

laplacetransform 3x

l a pl a ce t r an s f or m 3 x

integral of (x-9)/(x^2+3x-10)

\int \frac{x - 9}{x ^{2} + 3 x - 10} d x