integral of arctan((2x)/(1-x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die partielle Integration an

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

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

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

Füge eine Konstante zur Lösung hinzu

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

\frac{\partial}{\partial x} (1 + 3 x + 2 y^{2})

\frac{\partial}{\partial y} (\frac{y}{7 x})

\int_{1}^{4} (x) d x

\frac{d y}{d x} - \frac{y}{x} = 6 x e^{x}

y^{^{''}} + 4 y^{^{'}} + 4 y = t^{- 2} e^{- 2 t}