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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{2 x ^{3}}{3} + \frac{1}{4 x} - \frac{1}{2 x} + C

Schritte zur Lösung

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

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

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

= \frac{2 x ^{3}}{3} + \frac{1}{4 x} - \frac{1}{2 x}

Füge eine Konstante zur Lösung hinzu

= \frac{2 x ^{3}}{3} + \frac{1}{4 x} - \frac{1}{2 x} + C

Graph

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