integral of x^2arctan(4x)

Lösung

\int x^{2} arctan (4 x) d x

\frac{1}{3} x^{3} arctan (4 x) - \frac{1}{384} (16 x^{2} + 1 - ln 16 x^{2} + 1) + C

Schritte zur Lösung

\int x^{2} arctan (4 x) d x

Wende die partielle Integration an

= \frac{1}{3} x^{3} arctan (4 x) - \int \frac{4 x ^{3}}{3 ( 16 x ^{2} + 1 )} d x

\int \frac{4 x ^{3}}{3 ( 16 x ^{2} + 1 )} d x = \frac{1}{384} (16 x^{2} + 1 - ln 16 x^{2} + 1)

= \frac{1}{3} x^{3} arctan (4 x) - \frac{1}{384} (16 x^{2} + 1 - ln 16 x^{2} + 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arctan (4 x) - \frac{1}{384} (16 x^{2} + 1 - ln 16 x^{2} + 1) + C

\frac{d}{d x} (- 15)

\frac{\partial}{\partial y} (sin (4 y) e^{- 5 x})

\frac{d}{d x} (\frac{x ^{7} - 4 x ^{3} + 12 x}{x ^{3}})

x \to 0 lim (\frac{1}{e ^{x} - 1})

s l o p e (2, - 1), (8, 4)