integral of 3x^{-2/3}-2x^{5/3}

解答

\int 3 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

9 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}} + C

求解步骤

\int 3 x^{- \frac{2}{3}} - 2 x^{\frac{5}{3}} d x

使用积分加法定则:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 3 x^{- \frac{2}{3}} d x - \int 2 x^{\frac{5}{3}} d x

\int 3 x^{- \frac{2}{3}} d x = 9 x^{\frac{1}{3}}

\int 2 x^{\frac{5}{3}} d x = \frac{3}{4} x^{\frac{8}{3}}

= 9 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}}

解答补常数

= 9 x^{\frac{1}{3}} - \frac{3}{4} x^{\frac{8}{3}} + C

\int e^{\frac{- 1}{2} l n (x)} d x

\int \frac{1}{u ^{2} + 9} d u

\frac{d}{d x} (lo g_{e} (sin (x)))

l a pl a ce t r an s f or m t (t cos (t) - sin (t))

x \to 2 lim (\frac{x ^{2} - 3 x + 2}{x ^{2} + 5 x - 14})