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Beliebt Rechnen >

integral of 3arctan(x)

Lösung

\int 3 arctan (x) d x

Lösung

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

Schritte zur Lösung

\int 3 arctan (x) d x

Entferne die Konstante:

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

= 3 \cdot \int arctan (x) d x

Wende die partielle Integration an

= 3 (x arctan (x) - \int \frac{x}{x ^{2} + 1} d x)

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

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

Füge eine Konstante zur Lösung hinzu

= 3 (x arctan (x) - \frac{1}{2} ln x^{2} + 1) + C

Graph

Beliebte Beispiele

derivative 5x^2+1/(x^2)

d er i v a t i v e 5 x^{2} + \frac{1}{x ^{2}}

derivative (x+1)/(x^3+x-3)

d er i v a t i v e \frac{x + 1}{x ^{3} + x - 3}

limit as x approaches 1 of xln(x)

x \to 1 lim (x ln (x))

integral of 1/(x+2)

\int \frac{1}{x + 2} d x

derivative of sqrt(2-5x)

\frac{d}{d x} (2 - 5 x)