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Beliebt Rechnen >

integral of (x*arctan(x))

Lösung

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

Lösung

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

Schritte zur Lösung

\int x arctan (x) d x

Wende die partielle Integration an

= \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)

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

Füge eine Konstante zur Lösung hinzu

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

Graph

Beliebte Beispiele

integral of x^2+3x+5

\int x^{2} + 3 x + 5 d x

integral of (21x^2)/(4(x^3+5)^{5/4)}

\int \frac{21 x ^{2}}{4 ( x ^{3} + 5 ) ^{\frac{5}{4}}} d x

integral of (6x-2)

\int (6 x - 2) d x

integral of (sin(x))^4(cos(x))^3

\int (sin (x))^{4} (cos (x))^{3} d x

integral of 2(ln(x))

\int 2 (ln (x)) d x