integral ((4+12x))/4

Lösung

integral

\frac{( 4 + 12 x )}{4}

\frac{1}{2} x (3 x + 2) + C

Schritte zur Lösung

\int \frac{4 + 12 x}{4} d x

Entferne die Konstante:

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

= \frac{1}{4} \cdot \int 4 + 12 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

= \frac{1}{4} (\int 4 d x + \int 12 x d x)

\int 4 d x = 4 x

\int 12 x d x = 6 x^{2}

= \frac{1}{4} (4 x + 6 x^{2})

Vereinfache

\frac{1}{4} (4 x + 6 x^{2}) : \frac{1}{2} x (3 x + 2)

= \frac{1}{2} x (3 x + 2)

Füge eine Konstante zur Lösung hinzu

= \frac{1}{2} x (3 x + 2) + C

in t e g r a l (e^{x})^{- 2}

in t e g r a l \frac{x ^{2} + x + 1}{x}

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in t e g r a l (9 x + 4)^{4}