integral of (2xsin(y)-ysin(x))

解答

\int (2 x sin (y) - y sin (x)) d x

y cos (x) + x^{2} sin (y) + C

求解步骤

\int 2 x sin (y) - y sin (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 sin (x) y d x + \int 2 sin (y) x d x

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

\int 2 sin (y) x d x = x^{2} sin (y)

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

化简

= y cos (x) + x^{2} sin (y)

解答补常数

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

\frac{d}{d x} ((8 x^{2} - 14 x) e^{x})

\int_{1}^{25} e^{x} d x

\frac{d}{d x} (ln ((x + 3)^{4}))

y^{^{''}} + 4 y^{^{'}} - 12 y = 0

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