integral of (x-1)cos(x/3)

解答

\int (x - 1) cos (\frac{x}{3}) d x

3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) - 3 sin (\frac{x}{3}) + C

求解步骤

\int (x - 1) cos (\frac{x}{3}) d x

乘开

(x - 1) cos (\frac{x}{3}) : x cos (\frac{x}{3}) - cos (\frac{x}{3})

= \int x cos (\frac{x}{3}) - cos (\frac{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 x cos (\frac{x}{3}) d x - \int cos (\frac{x}{3}) d x

\int x cos (\frac{x}{3}) d x = 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3})

\int cos (\frac{x}{3}) d x = 3 sin (\frac{x}{3})

= 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) - 3 sin (\frac{x}{3})

解答补常数

= 3 x sin (\frac{x}{3}) + 9 cos (\frac{x}{3}) - 3 sin (\frac{x}{3}) + C

\frac{d}{d x} (x^{0.2})

d er i v a t i v e e^{6 s i n (7 x)}

\frac{d}{d x} (\frac{π}{3})

\int \frac{1}{7 + 8 x ^{2}} d x

n = 0 \sum \infty n! (x - 4)^{n}