What is the integral of (1/y sin(x/y)+x) ?

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

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integral of (1/y sin(x/y)+x)

\int (\frac{1}{y} sin (\frac{x}{y}) + x) d x

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

Solution steps

\int \frac{1}{y} sin (\frac{x}{y}) + x 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 x d x + \int \frac{1}{y} sin (\frac{x}{y}) d x

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (arctan (e^{x} + 1))

\int_{- 1}^{2} (x^{2} - x - 2) d x

x \to - 5 lim (\frac{x ^{2}}{5 - x})

\frac{d}{d x} (\frac{9}{x ^{4}})

3 x^{2}, - 3 x + 6, - 4, 2

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