integral of-2+12x-12x^2

解答

\int - 2 + 12 x - 12 x^{2} d x

- 2 x + 6 x^{2} - 4 x^{3} + C

求解步骤

\int - 2 + 12 x - 12 x^{2} 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 2 d x + \int 12 x d x - \int 12 x^{2} d x

\int 2 d x = 2 x

\int 12 x d x = 6 x^{2}

\int 12 x^{2} d x = 4 x^{3}

= - 2 x + 6 x^{2} - 4 x^{3}

解答补常数

= - 2 x + 6 x^{2} - 4 x^{3} + C

\int \frac{e ^{8 x}}{e ^{8 x} + 4} d x

t an g e n t f (x) = x^{2} + 3 x - 1, at x = 0

x \to 0 - lim (x \cdot ln (x))

\frac{d}{d x} (\frac{6 x + y}{x ^{2} + y ^{2}})

x \to 3 lim (\frac{x - 3}{x ^{2} - 3})