integral x^2*arctan(x)

Lösung

integral

x^{2} \cdot arctan (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

in t e g r a l \frac{lo g _{10} ( ( 1 + x ) ^{2} )}{x ^{2}}

in t e g r a l \frac{1}{( x ln ( x ) )}

in t e g r a l \frac{2 sin ( x )}{cos ^{2} ( x )}

in t e g r a l (2 x + 5)^{5}

in t e g r a l \frac{x}{( x ^{2} + 3 )}