integral of x^2*arctan(x)

Lösung

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

\frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1) + C

Schritte zur Lösung

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

Wende die partielle Integration an

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

\int \frac{x ^{3}}{3 ( x ^{2} + 1 )} d x = \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1)

= \frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{3} x^{3} arctan (x) - \frac{1}{6} (x^{2} + 1 - ln x^{2} + 1) + C

\int_{1}^{x} t^{2} d t

s l o p e x y - 8 y^{2} = 4, (18, 2)

l a pl a ce t r an s f or m 5 + 2 t cos (2 t)

d er i v a t i v e f (x) = 2^{2^{x}}

\int_{1}^{6} \frac{4}{x} d x