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Beliebt Rechnen >

integral of arctan(2y)

Lösung

\int arctan (2 y) d y

Lösung

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

Schritte zur Lösung

\int arctan (2 y) d y

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

limit as x approaches 0 of 1/x+1/(x^2)

x \to 0 lim (\frac{1}{x} + \frac{1}{x ^{2}})

limit as n approaches 0 of ln(n)

n \to 0 lim (ln (n))

integral of x/(x^2+8)

\int \frac{x}{x ^{2} + 8} d x

derivative of 12x^2-2x^3

\frac{d}{d x} (12 x^{2} - 2 x^{3})

fläche f(x)=x^3-x,[0,3]

a re a f (x) = x^{3} - x, [0, 3]