de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of (x^4)/(3x^2+27)

Lösung

\int \frac{x ^{4}}{3 x ^{2} + 27} d x

Lösung

\frac{x ^{3}}{9} - 3 x + 9 arctan (\frac{x}{3}) + C

Schritte zur Lösung

\int \frac{x ^{4}}{3 x ^{2} + 27} d x

Lange Division

\frac{x ^{4}}{3 x ^{2} + 27} : \frac{x ^{2}}{3} - 3 + \frac{27}{x ^{2} + 9}

= \int \frac{x ^{2}}{3} - 3 + \frac{27}{x ^{2} + 9} 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{x ^{2}}{3} d x - \int 3 d x + \int \frac{27}{x ^{2} + 9} d x

\int \frac{x ^{2}}{3} d x = \frac{x ^{3}}{9}

\int 3 d x = 3 x

\int \frac{27}{x ^{2} + 9} d x = 9 arctan (\frac{x}{3})

= \frac{x ^{3}}{9} - 3 x + 9 arctan (\frac{x}{3})

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{9} - 3 x + 9 arctan (\frac{x}{3}) + C

Graph

Beliebte Beispiele

integral of (2x^2-2)sin(2x)

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

integral of 1/(sqrt((x+2)(3-x)))

integral of (4x+3)(ln(2x-3))

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