integral of 4/15 x^{5/2}+9cos(x)+Cx+C

解答

\int \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x + C d x

\frac{8}{105} x^{\frac{7}{2}} + 9 sin (x) + \frac{C x ^{2}}{2} + C x + C

求解步骤

\int \frac{4}{15} x^{\frac{5}{2}} + 9 cos (x) + C x + C 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 9 cos (x) d x + \int C x d x + \int C d x

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

\int 9 cos (x) d x = 9 sin (x)

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

\int C d x = C x

= \frac{8}{105} x^{\frac{7}{2}} + 9 sin (x) + \frac{C x ^{2}}{2} + C x

解答补常数

= \frac{8}{105} x^{\frac{7}{2}} + 9 sin (x) + \frac{C x ^{2}}{2} + C x + C

\int \frac{1}{x ^{2}} + \frac{1}{x} d x

\frac{d}{d x} (ln (ln (6 x)))

\frac{d}{d x} (x^{2} ln (\frac{1}{x}))

\frac{\partial}{\partial x} (9 cos (x y) x)

d er i v a t i v e sin^{2} (x^{2} - 1)