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Beliebt Rechnen >

integral of 2xarctan(x)

Lösung

\int 2 x arctan (x) d x

Lösung

x^{2} arctan (x) + arctan (x) - x + C

Schritte zur Lösung

\int 2 x arctan (x) d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 2 \cdot \int x arctan (x) d x

Wende die partielle Integration an

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

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

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

Vereinfache

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

= x^{2} arctan (x) + arctan (x) - x

Füge eine Konstante zur Lösung hinzu

= x^{2} arctan (x) + arctan (x) - x + C

Graph

Beliebte Beispiele

(dy)/(dx)= x/(10y)

\frac{d y}{d x} = \frac{x}{10 y}

tangent y=2x^3-x^2+1,(2,13)

t an g e n t y = 2 x^{3} - x^{2} + 1, (2, 13)

derivative of (pisqrt(8100+x^2)/x)

\frac{d}{d x} (\frac{π 8100 + x ^{2}}{x})

derivative 4/(x+10)

d er i v a t i v e \frac{4}{x + 10}

limit as x approaches+1+of 5/(x^3-1)

x \to + 1 + lim (\frac{5}{x ^{3} - 1})