integral of 3sin(x/2)-2cos((2x)/5)

解答

\int 3 sin (\frac{x}{2}) - 2 cos (\frac{2 x}{5}) d x

- 6 cos (\frac{x}{2}) - 5 sin (\frac{2 x}{5}) + C

求解步骤

\int 3 sin (\frac{x}{2}) - 2 cos (\frac{2 x}{5}) 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 3 sin (\frac{x}{2}) d x - \int 2 cos (\frac{2 x}{5}) d x

\int 3 sin (\frac{x}{2}) d x = - 6 cos (\frac{x}{2})

\int 2 cos (\frac{2 x}{5}) d x = 5 sin (\frac{2 x}{5})

= - 6 cos (\frac{x}{2}) - 5 sin (\frac{2 x}{5})

解答补常数

= - 6 cos (\frac{x}{2}) - 5 sin (\frac{2 x}{5}) + C

\frac{d}{d x} (2 x y^{2} + 4)

\frac{d}{d x} ((1 + 3 x)^{5})

\int \frac{1}{X ^{2}} d X

\int \frac{5 x ^{2} - 12}{( x ^{2} - 6 x + 13 ) ^{2}} d x

\int \frac{4 x}{x ^{3} - x ^{2} - x + 1} d x