What is the integral of (x+(sin(2x))/y) ?

The integral of (x+(sin(2x))/y) is -1/(2y)cos(2x)+(x^2)/2+C

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

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

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

Solution steps

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

Apply the Sum Rule:

\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}

Add a constant to the solution

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

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What is the integral of (x+(sin(2x))/y) ?
The integral of (x+(sin(2x))/y) is -1/(2y)cos(2x)+(x^2)/2+C