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^2+3)3x^2

Lösung

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

Lösung

3 (\frac{x ^{5}}{5} + x^{3}) + C

Schritte zur Lösung

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

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

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

Multipliziere aus

(x^{2} + 3) x^{2} : x^{4} + 3 x^{2}

= 3 \cdot \int x^{4} + 3 x^{2} 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

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

\int x^{4} d x = \frac{x ^{5}}{5}

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

= 3 (\frac{x ^{5}}{5} + x^{3})

Füge eine Konstante zur Lösung hinzu

= 3 (\frac{x ^{5}}{5} + x^{3}) + C

Graph

Beliebte Beispiele

integral of (x+2)/((x^2+4x+1)^2)

\int \frac{x + 2}{( x ^{2} + 4 x + 1 ) ^{2}} d x

integral of ln(13x)

\int ln (13 x) d x

integral of-e^{-x}sin(x)

\int - e^{- x} sin (x) d x

integral of x^3(7+x^4)^7

\int x^{3} (7 + x^{4})^{7} d x

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

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