integral of 7x-sqrt(x)

解答

\int 7 x - x d x

\frac{7 x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}} + C

求解步骤

\int 7 x - x 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 7 x d x - \int x d x

\int 7 x d x = \frac{7 x ^{2}}{2}

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

= \frac{7 x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}}

解答补常数

= \frac{7 x ^{2}}{2} - \frac{2}{3} x^{\frac{3}{2}} + C

d er i v a t i v e y = ln (- 3 x^{6})

(1 + y^{2}) d x - (x^{2} + 1) d y = 0

\frac{\partial}{\partial x} (\frac{- y ^{4}}{4 x ^{4}})

\int (\frac{1}{1 - x}) d x

t an g e n t f (x) = 2 x^{2} + 2 x, (- 2, - 6)