integral of \sqrt[8]{x}+\sqrt[9]{x}

Lösung

\int 8 x + 9 x d x

\frac{8}{9} x^{\frac{9}{8}} + \frac{9}{10} x^{\frac{10}{9}} + C

Schritte zur Lösung

\int 8 x + 9 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 8 x d x + \int 9 x d x

\int 8 x d x = \frac{8}{9} x^{\frac{9}{8}}

\int 9 x d x = \frac{9}{10} x^{\frac{10}{9}}

= \frac{8}{9} x^{\frac{9}{8}} + \frac{9}{10} x^{\frac{10}{9}}

Füge eine Konstante zur Lösung hinzu

= \frac{8}{9} x^{\frac{9}{8}} + \frac{9}{10} x^{\frac{10}{9}} + C

d er i v a t i v e f (x) = (t^{6} + 1)^{500}

t an g e n t - \frac{x}{( 25 - x ^{2} ) ^{\frac{1}{2}}}

d er i v a t i v e (125 + x)^{- \frac{1}{3}}

\int cos^{3} (3 x) d x

y^{^{'}} = \frac{y}{( x ^{2} + 1 ) x}