integral of 8x^{3/5}+5x^{-4/5}

Lösung

\int 8 x^{\frac{3}{5}} + 5 x^{- \frac{4}{5}} d x

5 x^{\frac{8}{5}} + 25 x^{\frac{1}{5}} + C

Schritte zur Lösung

\int 8 x^{\frac{3}{5}} + 5 x^{- \frac{4}{5}} d x

5 x^{- \frac{4}{5}} = \frac{5}{x ^{\frac{4}{5}}}

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

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

\int \frac{5}{x ^{\frac{4}{5}}} d x = 25 x^{\frac{1}{5}}

= 5 x^{\frac{8}{5}} + 25 x^{\frac{1}{5}}

Füge eine Konstante zur Lösung hinzu

= 5 x^{\frac{8}{5}} + 25 x^{\frac{1}{5}} + C

\int \frac{48 x ^{2}}{( x - 15 ) ( x + 5 ) ^{2}} d x

\frac{d}{d t} (- 6 t)

in v erse l a pl a ce \frac{2 x}{x ^{2} + 2 x} + x + 5

y^{^{''}} - 14 y^{^{'}} + 48 y = 0

\int x + 10 d x