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Beliebt Rechnen >

integral of (x^2+3sqrt(x)-4/(x^2)+2+x)

Lösung

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

Lösung

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

Schritte zur Lösung

\int x^{2} + 3 x - \frac{4}{x ^{2}} + 2 + 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

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

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

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

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

\int 2 d x = 2 x

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

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

Vereinfache

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

Füge eine Konstante zur Lösung hinzu

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

Graph

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