integral of xarctan(8x)

Lösung

\int x arctan (8 x) d x

\frac{1}{2} x^{2} arctan (8 x) - \frac{1}{128} (- arctan (8 x) + 8 x) + C

Schritte zur Lösung

\int x arctan (8 x) d x

Wende die partielle Integration an

= \frac{1}{2} x^{2} arctan (8 x) - \int \frac{4 x ^{2}}{64 x ^{2} + 1} d x

\int \frac{4 x ^{2}}{64 x ^{2} + 1} d x = \frac{1}{128} (- arctan (8 x) + 8 x)

= \frac{1}{2} x^{2} arctan (8 x) - \frac{1}{128} (- arctan (8 x) + 8 x)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x^{2} arctan (8 x) - \frac{1}{128} (- arctan (8 x) + 8 x) + C

f (x) = cos^{2} (4 x)

\frac{d}{d x} ((6 x + e^{- x^{2}})^{5})

x \to 0 lim (\frac{2 x}{sin ( x )})

\int \frac{60 x ^{2} + 20 x}{10 x ^{3} + 5 x ^{2} + 3} d x

d er i v a t i v e y = x x