integral of 1-sqrt(x)

解答

\int 1 - x d x

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

求解步骤

\int 1 - 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 1 d x - \int x d x

\int 1 d x = x

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

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

解答补常数

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

\int (3 x^{4} - 4 x^{3} + 6 x^{2} - \frac{x}{2} + 3) d x

\int 8 tan (x) sin (y) cos (y) d x

\frac{d}{d x} ((2 x^{2} - 7)^{5} - (1 + 4 x^{3})^{5})

d er i v a t i v e \frac{3 x}{e ^{x}}

(x \cdot e^{x})^{^{'}}