integral of (2sin(x)-pi/4 x)

解答

\int (2 sin (x) - \frac{π}{4} x) d x

- 2 cos (x) - \frac{π x ^{2}}{8} + C

求解步骤

\int 2 sin (x) - \frac{π}{4} x 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 2 sin (x) d x - \int \frac{π}{4} x d x

\int 2 sin (x) d x = - 2 cos (x)

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

= - 2 cos (x) - \frac{π x ^{2}}{8}

解答补常数

= - 2 cos (x) - \frac{π x ^{2}}{8} + C

\frac{d}{d x} (ln (\frac{x}{x}))

\frac{d}{d t} (a cos^{3} (t))

t an g e n t f (x) = x^{2} + 21, at x = 2

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

\frac{d y}{d x} = \frac{- 2 x}{y}