de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

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

Lösung

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

Lösung

ln ∣ x ∣ + arctan (x) + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

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

= ln ∣ x ∣ + arctan (x)

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ + arctan (x) + C

Graph

Beliebte Beispiele

integral of sh(x)

integral of x^2-45

integral of (ln(arcsin(x)))/(sqrt(1-x^2))

integral of sin(t)+3cos(t)

integral of ((x+9))/x