integral of (5x^2+4sqrt(x)+1/(x^3))

Lösung

\int (5 x^{2} + 4 x + \frac{1}{x ^{3}}) d x

\frac{5 x ^{3}}{3} + \frac{8}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

Schritte zur Lösung

\int 5 x^{2} + 4 x + \frac{1}{x ^{3}} 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 5 x^{2} d x + \int 4 x d x + \int \frac{1}{x ^{3}} d x

\int 5 x^{2} d x = \frac{5 x ^{3}}{3}

\int 4 x d x = \frac{8}{3} x^{\frac{3}{2}}

\int \frac{1}{x ^{3}} d x = - \frac{1}{2 x ^{2}}

= \frac{5 x ^{3}}{3} + \frac{8}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}}

Füge eine Konstante zur Lösung hinzu

= \frac{5 x ^{3}}{3} + \frac{8}{3} x^{\frac{3}{2}} - \frac{1}{2 x ^{2}} + C

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