integral of 4/15 x^{5/2}+6cos(x)+Cx+D

解答

\int \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + D d x

\frac{8}{105} x^{\frac{7}{2}} + 6 sin (x) + \frac{C x ^{2}}{2} + D x + C

求解步骤

\int \frac{4}{15} x^{\frac{5}{2}} + 6 cos (x) + C x + D 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 \frac{4}{15} x^{\frac{5}{2}} d x + \int 6 cos (x) d x + \int C x d x + \int D d x

\int \frac{4}{15} x^{\frac{5}{2}} d x = \frac{8}{105} x^{\frac{7}{2}}

\int 6 cos (x) d x = 6 sin (x)

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

\int D d x = D x

= \frac{8}{105} x^{\frac{7}{2}} + 6 sin (x) + \frac{C x ^{2}}{2} + D x

解答补常数

= \frac{8}{105} x^{\frac{7}{2}} + 6 sin (x) + \frac{C x ^{2}}{2} + D x + C

\frac{d}{d x} (x^{7} ln (3 x))

d er i v a t i v e \frac{4 x}{9 - cot ( x )}

\int y e^{2 x y} + x d x

x \to 0 lim (\frac{e ^{- 7 x} - 1}{x})

\frac{d}{d x} (\frac{( a x + b )}{c x + d})