integral of (2x-3)(5x+1)

解答

\int (2 x - 3) (5 x + 1) d x

\frac{10 x ^{3}}{3} - \frac{13 x ^{2}}{2} - 3 x + C

求解步骤

\int (2 x - 3) (5 x + 1) d x

乘开

(2 x - 3) (5 x + 1) : 10 x^{2} - 13 x - 3

= \int 10 x^{2} - 13 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 10 x^{2} d x - \int 13 x d x - \int 3 d x

\int 10 x^{2} d x = \frac{10 x ^{3}}{3}

\int 13 x d x = \frac{13 x ^{2}}{2}

\int 3 d x = 3 x

= \frac{10 x ^{3}}{3} - \frac{13 x ^{2}}{2} - 3 x

解答补常数

= \frac{10 x ^{3}}{3} - \frac{13 x ^{2}}{2} - 3 x + C

\int_{1}^{5} \frac{4}{x} d x

n = 1 \sum \infty \frac{2}{3 ^{n} + 1}

y^{^{'}} = (1 - 2 x) y^{2}, y (0) = - \frac{1}{30}

\int_{0}^{8} k (8 - x)

d er i v a t i v e f (x) = - 6 x^{2} + 7 x