de

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Beliebt Rechnen >

integral of ((3x^2+9x+1))/x

Lösung

\int \frac{( 3 x ^{2} + 9 x + 1 )}{x} d x

Lösung

\frac{3 x ^{2}}{2} + 9 x + ln ∣ x ∣ + C

Schritte zur Lösung

\int \frac{3 x ^{2} + 9 x + 1}{x} d x

Multipliziere aus

\frac{3 x ^{2} + 9 x + 1}{x} : 3 x + 9 + \frac{1}{x}

= \int 3 x + 9 + \frac{1}{x} 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 3 x d x + \int 9 d x + \int \frac{1}{x} d x

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

\int 9 d x = 9 x

\int \frac{1}{x} d x = ln ∣ x ∣

= \frac{3 x ^{2}}{2} + 9 x + ln ∣ x ∣

Füge eine Konstante zur Lösung hinzu

= \frac{3 x ^{2}}{2} + 9 x + ln ∣ x ∣ + C

Graph

Beliebte Beispiele

integral of (sin(2x))/(2+3cos(2x))

\int \frac{sin ( 2 x )}{2 + 3 cos ( 2 x )} d x

integral of (x+3/x)^2

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

integral of sec^7(3x)

\int sec^{7} (3 x) d x

integral of 3xe^{(x^2)/2}

\int 3 x e^{\frac{x ^{2}}{2}} d x

integral of tan^4(x)sec^3(x)tan(x)sec(x)

\int tan^{4} (x) sec^{3} (x) tan (x) sec (x) d x