integral of e^{2y}-ycos(xy)

解答

\int e^{2 y} - y cos (x y) d x

e^{2 y} x - sin (y x) + C

求解步骤

\int e^{2 y} - y cos (x y) 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 e^{2 y} d x - \int cos (y x) y d x

\int e^{2 y} d x = e^{2 y} x

\int cos (y x) y d x = sin (y x)

= e^{2 y} x - sin (y x)

解答补常数

= e^{2 y} x - sin (y x) + C

\frac{d}{d x} (4.9 x^{2})

\frac{\partial}{\partial x} (ln (\frac{x - 2}{3}))

x \to 7 lim (\frac{x - 7}{∣ x - 7 ∣})

x \to 0 lim (x^{2} + 3 x + 1)

y^{^{''}} + 4 y^{^{'}} + 3 y = 0, y (0) = 2, y^{^{'}} (0) = - 1