de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

integral

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

Lösung

- arctan (r) + r + C

Schritte zur Lösung

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

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

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

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 + r ^{2}} d r + \int 1 d r

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

\int 1 d r = r

= - arctan (r) + r

Füge eine Konstante zur Lösung hinzu

= - arctan (r) + r + C

Graph

Beliebte Beispiele

integral (1-sin^2(x))/(sin^2(x))

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

integral 1/((3x^2-4x))

in t e g r a l \frac{1}{( 3 x ^{2} - 4 x )}

integral 0.75^x

in t e g r a l 0.7 5^{x}

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

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

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