integral of (x+3)(x-7)

解答

\int (x + 3) (x - 7) d x

\frac{x ^{3}}{3} - 2 x^{2} - 21 x + C

求解步骤

\int (x + 3) (x - 7) d x

乘开

(x + 3) (x - 7) : x^{2} - 4 x - 21

= \int x^{2} - 4 x - 21 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 x^{2} d x - \int 4 x d x - \int 21 d x

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

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

\int 21 d x = 21 x

= \frac{x ^{3}}{3} - 2 x^{2} - 21 x

解答补常数

= \frac{x ^{3}}{3} - 2 x^{2} - 21 x + C

a re a x^{2} - 3, 5 - x^{2}

\frac{\partial}{\partial x} (x^{2} + 2 y^{2} + x y^{2} + 1)

f (t) = 3 sin (2 t)

\int x^{2} - 5 x + 6 d x

\frac{\partial}{\partial x} (x^{\frac{1}{4}} y^{\frac{3}{4}})