integral of (x+(sin(2x))/y)

解答

\int (x + \frac{sin ( 2 x )}{y}) d x

- \frac{1}{2 y} cos (2 x) + \frac{x ^{2}}{2} + C

求解步骤

\int x + \frac{sin ( 2 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 \frac{sin ( 2 x )}{y} d x + \int x d x

\int \frac{sin ( 2 x )}{y} d x = - \frac{1}{2 y} cos (2 x)

\int x d x = \frac{x ^{2}}{2}

= - \frac{1}{2 y} cos (2 x) + \frac{x ^{2}}{2}

解答补常数

= - \frac{1}{2 y} cos (2 x) + \frac{x ^{2}}{2} + C

d er i v a t i v e f (x) = (8 x - 7)^{\frac{1}{2}}

\frac{d y}{d x} = e^{4 x + 5 y}

\int_{3}^{5} \frac{y ^{2}}{2} + \frac{1}{2 y ^{2}} d y

\int x^{3} - 3 x^{- 4} - 2 d x

\int x^{2} lo g_{e} (x) d x