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

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

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integral of (x+sin(y))

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

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

Solution steps

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

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

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

= sin (y) x + \frac{x ^{2}}{2}

Add a constant to the solution

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

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