integral (x^2)/((1+x^2))

Lösung

integral

\frac{x ^{2}}{( 1 + x ^{2} )}

- arctan (x) + x + C

Schritte zur Lösung

\int \frac{x ^{2}}{1 + x ^{2}} d x

\frac{x ^{2}}{1 + x ^{2}} = - \frac{1}{1 + x ^{2}} + 1

= \int - \frac{1}{1 + x ^{2}} + 1 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= - \int \frac{1}{1 + x ^{2}} d x + \int 1 d x

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

\int 1 d x = x

= - arctan (x) + x

Füge eine Konstante zur Lösung hinzu

= - arctan (x) + x + C

in t e g r a l (1 - n) cos (x)

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

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

in t e g r a l \frac{1}{( sin ^{2} ( x ) \cdot cos ^{4} ( x ) )}

in t e g r a l \frac{( x ^{2} - x - 2 )}{( 1 - x ^{2} )}