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+2x^2)

Lösung

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

Lösung

ln ∣ x ∣ - ln ∣ 2 x + 1 ∣ + C

Schritte zur Lösung

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

Ermittle den Partialbruch von

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

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

\int \frac{1}{x} d x = ln ∣ x ∣

\int \frac{2}{2 x + 1} d x = ln ∣ 2 x + 1 ∣

= ln ∣ x ∣ - ln ∣ 2 x + 1 ∣

Füge eine Konstante zur Lösung hinzu

= ln ∣ x ∣ - ln ∣ 2 x + 1 ∣ + C

Graph

Beliebte Beispiele

integral of (ln(x)+xln(x))

\int (ln (x) + x ln (x)) d x

integral of (x^2+3sqrt(x)-4/(x^2)+2+x)

\int (x^{2} + 3 x - \frac{4}{x ^{2}} + 2 + x) d x

integral of 18(3x+4)^5

\int 18 (3 x + 4)^{5} d x

integral of (1+ln(x))/(2+xln(x))

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

integral of 3x^2y^2-10xy^2

\int 3 x^{2} y^{2} - 10 x y^{2} d x