integral of (2x-5sqrt(x))^2

Lösung

\int (2 x - 5 x)^{2} d x

\frac{4 x ^{3}}{3} - 8 x^{\frac{5}{2}} + \frac{25 x ^{2}}{2} + C

Schritte zur Lösung

\int (2 x - 5 x)^{2} d x

Multipliziere aus

(2 x - 5 x)^{2} : 4 x^{2} - 20 x^{\frac{3}{2}} + 25 x

= \int 4 x^{2} - 20 x^{\frac{3}{2}} + 25 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 4 x^{2} d x - \int 20 x^{\frac{3}{2}} d x + \int 25 x d x

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

\int 20 x^{\frac{3}{2}} d x = 8 x^{\frac{5}{2}}

\int 25 x d x = \frac{25 x ^{2}}{2}

= \frac{4 x ^{3}}{3} - 8 x^{\frac{5}{2}} + \frac{25 x ^{2}}{2}

Füge eine Konstante zur Lösung hinzu

= \frac{4 x ^{3}}{3} - 8 x^{\frac{5}{2}} + \frac{25 x ^{2}}{2} + C

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