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

Lösung

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

- \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3} + C

Schritte zur Lösung

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

\int 4 x^{\frac{3}{2}} d x = \frac{8}{5} x^{\frac{5}{2}}

\int 3 x^{\frac{2}{3}} d x = \frac{9}{5} x^{\frac{5}{3}}

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

= - \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3}

Füge eine Konstante zur Lösung hinzu

= - \frac{8}{5} x^{\frac{5}{2}} + \frac{9}{5} x^{\frac{5}{3}} - \frac{4 x ^{3}}{3} + C

\frac{\partial}{\partial z} (sin (y))

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\int \frac{10 X}{X ^{4} - 13 X ^{2} + 36} d X

d er i v a t i v e x^{\frac{8}{x}}

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