integral of (2x^{-1}+3x^2)

Lösung

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

2 ln ∣ x ∣ + x^{3} + C

Schritte zur Lösung

\int 2 x^{- 1} + 3 x^{2} d x

2 x^{- 1} = \frac{2}{x}

= \int \frac{2}{x} + 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

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

\int \frac{2}{x} d x = 2 ln ∣ x ∣

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

= 2 ln ∣ x ∣ + x^{3}

Füge eine Konstante zur Lösung hinzu

= 2 ln ∣ x ∣ + x^{3} + C

\int \frac{12}{x 1 + 2 x} d x

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

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

\int (x + \frac{3 y}{x}) d x

\int \frac{1}{t} cos (t + 3) d t