integral of x^2+6x^{-3/2}

Lösung

\int x^{2} + 6 x^{- \frac{3}{2}} d x

\frac{x ^{3}}{3} - \frac{12}{x ^{\frac{1}{2}}} + C

Schritte zur Lösung

\int x^{2} + 6 x^{- \frac{3}{2}} d x

6 x^{- \frac{3}{2}} = \frac{6}{x ^{\frac{3}{2}}}

= \int x^{2} + \frac{6}{x ^{\frac{3}{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 x^{2} d x + \int \frac{6}{x ^{\frac{3}{2}}} d x

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

\int \frac{6}{x ^{\frac{3}{2}}} d x = - \frac{12}{x ^{\frac{1}{2}}}

= \frac{x ^{3}}{3} - \frac{12}{x ^{\frac{1}{2}}}

Füge eine Konstante zur Lösung hinzu

= \frac{x ^{3}}{3} - \frac{12}{x ^{\frac{1}{2}}} + C

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

x \to \infty lim (\frac{( 25 x + 7 ) 5 x ^{2} + 2}{5 x ^{2} + 2})

\int 1 4^{x} d x

t an g e n t f (x) = 4 + 3 ln (x), at x = 1

x \to 2 lim (\frac{1}{x})