integral of 7\sqrt[6]{x^5}

Lösung

\int 7 6 x^{5} d x

\frac{42}{11} x^{\frac{11}{6}} + C

Schritte zur Lösung

\int 7 6 x^{5} d x

Entferne die Konstante:

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

= 7 \cdot \int 6 x^{5} d x

6 x^{5} = x^{\frac{5}{6}},

angenommen

x \geq 0

= 7 \cdot \int x^{\frac{5}{6}} d x

Wende die Potenzregel an

= 7 \cdot \frac{6}{11} x^{\frac{11}{6}}

Vereinfache

7 \cdot \frac{6}{11} x^{\frac{11}{6}} : \frac{42}{11} x^{\frac{11}{6}}

= \frac{42}{11} x^{\frac{11}{6}}

Füge eine Konstante zur Lösung hinzu

= \frac{42}{11} x^{\frac{11}{6}} + C

\frac{d}{d x} (ln (cos (x)))

\int \frac{tan ^{2} ( x )}{sec ^{5} ( x )} d x

\int \frac{w}{16 - w ^{2}} d w

\frac{d}{d x} (\frac{x}{x ^{2} + 7})

x \to 0 lim (7 cot^{4} (3 x))