integral of 6x^2-8x+3

解答

\int 6 x^{2} - 8 x + 3 d x

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

求解步骤

\int 6 x^{2} - 8 x + 3 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 6 x^{2} d x - \int 8 x d x + \int 3 d x

\int 6 x^{2} d x = 2 x^{3}

\int 8 x d x = 4 x^{2}

\int 3 d x = 3 x

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

解答补常数

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

d er i v a t i v e x^{3} (3 - x)^{4}

\int 1 + (\frac{1}{x ^{\frac{1}{3}}})^{2} d x

\frac{d}{d x} (100 + x^{2})

d er i v a t i v e y = x 6^{x}

x (x + y) (\frac{d y}{d x}) + y (3 x + y) = 0