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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

integral of (x^6)/((9-x^7)^2)

\int \frac{x ^{6}}{( 9 - x ^{7} ) ^{2}} d x

integral of 1/(1-2sin(x))

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

integral of 2x(x^2-1)^{99}

\int 2 x (x^{2} - 1)^{99} d x

integral of e^x(2-e^x)^{10}

\int e^{x} (2 - e^{x})^{10} d x

integral of (8^x)

\int (8^{x}) d x