integral of xarctan(7x)

Lösung

\int x arctan (7 x) d x

\frac{1}{2} x^{2} arctan (7 x) - \frac{1}{98} (- arctan (7 x) + 7 x) + C

Schritte zur Lösung

\int x arctan (7 x) d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} arctan (7 x) - \int \frac{7 x ^{2}}{2 ( 49 x ^{2} + 1 )} d x

\int \frac{7 x ^{2}}{2 ( 49 x ^{2} + 1 )} d x = \frac{1}{98} (- arctan (7 x) + 7 x)

= \frac{1}{2} x^{2} arctan (7 x) - \frac{1}{98} (- arctan (7 x) + 7 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} arctan (7 x) - \frac{1}{98} (- arctan (7 x) + 7 x) + C

z \to 0 lim (\frac{sin ( z )}{z})

d er i v a t i v e f (x) = \frac{4}{x ^{5}}

d er i v a t i v e 11 e^{x^{2}}

\int - 1 (x - 4) d x

\frac{d}{d x} ((2 x^{2} + 7) (8 x - 4))