integral of 3sqrt(x)+(10)/(x^6)

解答

\int 3 x + \frac{10}{x ^{6}} d x

2 x^{\frac{3}{2}} - \frac{2}{x ^{5}} + C

求解步骤

\int 3 x + \frac{10}{x ^{6}} 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 d x + \int \frac{10}{x ^{6}} d x

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

\int \frac{10}{x ^{6}} d x = - \frac{2}{x ^{5}}

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

解答补常数

= 2 x^{\frac{3}{2}} - \frac{2}{x ^{5}} + C

\frac{d ^{2}}{d x ^{2}} (lo g_{10} (x))

d er i v a t i v e (5 x)^{\frac{1}{3}}

\frac{d}{d x} (\frac{- 4 x ^{5} - 2 π ^{2}}{x ^{7}})

\int 1 - cos (2 x) d x

\int u^{6} d u