What is the integral of 50+14sin((pix)/(12)) ?

The integral of 50+14sin((pix)/(12)) is 50x-(168)/pi cos((pix)/(12))+C

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integral of 50+14sin((pix)/(12))

\int 50 + 14 sin (\frac{π x}{12}) d x

50 x - \frac{168}{π} cos (\frac{π x}{12}) + C

Solution steps

\int 50 + 14 sin (\frac{π x}{12}) 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 50 d x + \int 14 sin (\frac{π x}{12}) d x

\int 50 d x = 50 x

\int 14 sin (\frac{π x}{12}) d x = - \frac{168}{π} cos (\frac{π x}{12})

= 50 x - \frac{168}{π} cos (\frac{π x}{12})

Add a constant to the solution

= 50 x - \frac{168}{π} cos (\frac{π x}{12}) + C

What is the integral of 50+14sin((pix)/(12)) ?
The integral of 50+14sin((pix)/(12)) is 50x-(168)/pi cos((pix)/(12))+C