integral of \sqrt[3]{27x^5}

Lösung

\int 3 27 x^{5} d x

\frac{9}{8} x^{\frac{8}{3}} + C

Schritte zur Lösung

\int 3 27 x^{5} d x

3 27 x^{5} = 327 3 x^{5}

= \int 327 3 x^{5} d x

Entferne die Konstante:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 327 \cdot \int 3 x^{5} d x

327 = 3

= 3 \cdot \int 3 x^{5} d x

3 x^{5} = x^{\frac{5}{3}},

angenommen

x \geq 0

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

Wende die Potenzregel an

= 3 \cdot \frac{3}{8} x^{\frac{8}{3}}

Vereinfache

3 \cdot \frac{3}{8} x^{\frac{8}{3}} : \frac{9}{8} x^{\frac{8}{3}}

= \frac{9}{8} x^{\frac{8}{3}}

Füge eine Konstante zur Lösung hinzu

= \frac{9}{8} x^{\frac{8}{3}} + C

t an g e n t f (x) = \frac{1}{x - 1}, (- 7, - \frac{1}{8})

a re a (x^{2} - 4), y = 0, x = - 4, x = 3

\int \frac{e ^{5 s i n (x)}}{sec ( x )} d x

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

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