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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

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

Füge eine Konstante zur Lösung hinzu

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

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