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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Graph

Beliebte Beispiele

integral of (x^{-6/5})

\int (x^{- \frac{6}{5}}) d x

integral of 4/(e^{-4x)}

\int \frac{4}{e ^{- 4 x}} d x

integral of-5x^2e^{-3/5 x}

\int - 5 x^{2} e^{- \frac{3}{5} x} d x

integral of 4/(e^{3x)}

\int \frac{4}{e ^{3 x}} d x

integral of cos^{18}(x)sin^3(x)

\int cos^{18} (x) sin^{3} (x) d x